A095648 -id:A095648

A095649

Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 8.

+10
8

139, 181, 241, 283, 421, 467, 811, 829, 953, 1021, 1051, 1153, 1259, 1307, 1699, 1723, 1831, 1879, 2029, 2089, 2143, 2221, 2251, 2297, 2357, 2423, 2621, 2731, 3001, 3191, 3347, 3361, 3583, 3769, 3823, 3853, 4139, 4219, 4231, 4243, 4261, 4273, 4339, 4373

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes that are second prime chords.

These come from music based on the prime differences where the chords are an even number of note steps from the primary note.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

m = 2; Prime[ 1 + Select[ Range[600], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)

Transpose[Select[Partition[Prime[Range[600]], 3, 1], #[[1]]+#[[3]]==2#[[2]]+ 8&]][[2]] (* Harvey P. Dale, Feb 26 2015 *)

CROSSREFS

Cf. A095419, A095420, A095648, A095650, A095651, A095672, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited by Robert G. Wilson v, Jul 14 2004

Description corrected by N. J. A. Sloane, Jul 19 2004

STATUS

approved

A095651

Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 16.

+10
8

523, 887, 1129, 2557, 3271, 3739, 3947, 4027, 4159, 4423, 4759, 4831, 5449, 6397, 6427, 6451, 7351, 7459, 8017, 8543, 8783, 8867, 9067, 9349, 10433, 10667, 11177, 11447, 11597, 11867, 12049, 13063, 13267, 13421, 13729, 14011, 14087, 14107

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes that are fourth prime chords.

These come from music based on the prime differences where the chords are an even number of note steps from the primary note.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

P:= select(isprime, [seq(i, i=1..20000, 2)]):

J:= select(i -> P[i-1]+P[i+1] = 2*P[i]+16, [$2..nops(P)-1]):

P[J]; # Robert Israel, Jun 10 2024

MATHEMATICA

m = 4; Prime[ 1 + Select[ Range[1700], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)

Select[Partition[Prime[Range[3000]], 3, 1], #[[1]]+#[[3]]==2#[[2]]+16&][[;; , 2]] (* Harvey P. Dale, Jul 08 2024 *)

CROSSREFS

Cf. A095419, A095420, A095648, A095649, A095650, A095672, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 14 2004

Edited by N. J. A. Sloane, Nov 07 2005

STATUS

approved

A095672

Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 4.

+10
8

31, 61, 73, 151, 271, 293, 337, 401, 433, 491, 547, 571, 577, 601, 743, 761, 839, 911, 1033, 1039, 1063, 1201, 1231, 1291, 1321, 1409, 1453, 1531, 1571, 1621, 1627, 2003, 2017, 2039, 2131, 2243, 2273, 2341, 2383, 2551, 2663, 2713, 2719, 2791, 3041, 3049

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes that are first prime chords.

These come from music based on the prime differences where the chords are an even number of note steps from the primary note.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

31 is a term because 29+37 = 2*31 + 4 = 66.

MAPLE

primes:= select(isprime, [seq(i, i=3..10000, 2)]):

L:= primes[1..-3]+primes[3..-1]-2*primes[2..-2]:

primes[select(t -> L[t-1]=4, [$2..nops(L)+1])]; # Robert Israel, Jun 28 2018

MATHEMATICA

m = 1; Prime[1 + Select[ Range[450], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)

Select[Partition[Prime[Range[500]], 3, 1], #[[1]]+#[[3]]==2#[[2]]+4&][[;; , 2]] (* Harvey P. Dale, Jan 31 2024 *)

CROSSREFS

Cf. A095419, A095420, A095648, A095649, A095650, A095651, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited by Robert G. Wilson v, Jul 14 2004

Description corrected by N. J. A. Sloane, Jul 19 2004

STATUS

approved

A095673

Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 12.

+10
8

1069, 1759, 1913, 3803, 4463, 4603, 8329, 9109, 9749, 11633, 12619, 12763, 15199, 16993, 17299, 17449, 19163, 20029, 20183, 21943, 22349, 22409, 22549, 22943, 23209, 23339, 24709, 25373, 26209, 26783, 26993, 28669, 28979, 29723, 29959

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes that are third prime chords.

These come from music based on the prime differences where the chords are an even number of note steps from the primary note.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

m = 3; Prime[1 + Select[ Range[3300], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)

Transpose[Select[Partition[Prime[Range[4000]], 3, 1], #[[1]]+#[[3]]== 2#[[2]] +12&]][[2]] (* Harvey P. Dale, Apr 18 2015 *)

CROSSREFS

Cf. A095419, A095420, A095648, A095649, A095650, A095651, A095672.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 14 2004

Edited by N. J. A. Sloane, Nov 07 2005

STATUS

approved

A095419

Indices of the primes in A095649: A095649(n) = prime(a(n)).

+10
7

34, 42, 53, 61, 82, 91, 141, 145, 162, 172, 177, 191, 205, 214, 266, 269, 282, 289, 308, 316, 324, 331, 335, 342, 350, 360, 381, 399, 431, 452, 472, 474, 502, 525, 531, 535, 570, 578, 580, 582, 585, 587, 593, 597, 609, 672, 687, 704, 728, 746, 773, 779, 790

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..53.

MATHEMATICA

m = 2; 1 + Select[ Range[800], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &] (* Robert G. Wilson v, Jul 14 2004 *)

CROSSREFS

Cf. A095420, A095648, A095649, A095650, A095651, A095672, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited by Robert G. Wilson v, Jul 14 2004

Edited by N. J. A. Sloane, Nov 07 2005

STATUS

approved

A095420

Indices of the primes in A095651: A095651(n) = prime(a(n)).

+10
7

99, 154, 189, 375, 462, 522, 548, 557, 573, 602, 641, 650, 721, 834, 836, 838, 937, 945, 1010, 1066, 1095, 1106, 1127, 1158, 1277, 1302, 1355, 1381, 1396, 1423, 1444, 1556, 1577, 1592, 1625, 1654, 1662, 1663, 1669, 1683, 1754, 1792, 1818, 1861, 1887, 1944

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

MATHEMATICA

m = 4; 1 + Select[ Range[2000], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &] (* Robert G. Wilson v, Jul 14 2004 *)

CROSSREFS

Cf. A095419, A095648, A095649, A095650, A095651, A095672, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 14 2004

Edited by N. J. A. Sloane, Nov 07 2005

STATUS

approved

A095650

Indices of the primes in A095673: A095673(n) = prime(a(n)).

+10
7

180, 274, 293, 529, 607, 623, 1045, 1130, 1203, 1399, 1508, 1523, 1775, 1960, 1989, 2007, 2174, 2266, 2284, 2460, 2502, 2508, 2521, 2560, 2591, 2603, 2736, 2799, 2881, 2939, 2961, 3124, 3153, 3223, 3243, 3285, 3357, 3419, 3420, 3434, 3561, 3574, 3642

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..43.

MATHEMATICA

m = 3; 1 + Select[ Range[4000], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &] (* Robert G. Wilson v, Jul 14 2004 *)

CROSSREFS

Cf. A095419, A095420, A095648, A095649, A095651, A095672, A095673.

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jul 02 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Jul 14 2004

Edited by N. J. A. Sloane, Nov 07 2005

STATUS

approved