A171517 -id:A171517

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A248368

Primes p such that 52*p + 1 is prime.

+10
2

3, 13, 31, 43, 73, 109, 139, 151, 181, 193, 211, 223, 229, 283, 349, 379, 409, 421, 463, 523, 601, 619, 691, 769, 823, 853, 1021, 1033, 1069, 1153, 1231, 1279, 1303, 1453, 1459, 1471, 1531, 1663, 1693, 1723, 1741, 1783, 1831, 1873, 1933, 2029, 2131, 2251, 2269, 2293, 2593, 2671, 2749, 2791

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

OFFSET

1,1

COMMENTS

Or, primes in A248221. Subsequence of A248221. Note that a(1..6) coincide with A171517(1..6).

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

MAPLE

A248368:=n->`if`(isprime(52*n+1) and isprime(n), n, NULL): seq(A248368(n), n=1..4000); # Wesley Ivan Hurt, Oct 05 2014

MATHEMATICA

s = {}; Do[If[PrimeQ[1 + 52*(p = Prime[n])], AppendTo[s, p]], {n, 500}]; s

Select[Prime[Range[500]], PrimeQ[52#+1]&] (* Harvey P. Dale, Aug 15 2017 *)

PROG

(PARI)

forprime(p=1, 10^4, if(isprime(52*p+1), print1(p, ", "))) \\ Derek Orr, Oct 05 2014

CROSSREFS

Cf. A033210, A142508, A171517, A248221.

KEYWORD

nonn,easy

AUTHOR

Zak Seidov, Oct 05 2014

STATUS

approved

A290839

a(n) = smallest prime p such that 2p + 2n - 1 is prime.

+10
2

2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 3, 2, 7, 3, 2, 5, 3, 2, 2, 7, 3, 2, 3, 2, 2, 13, 3, 2, 3, 2, 11, 3, 2, 5, 7, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 13, 7, 11, 5, 19, 3, 2, 3, 2, 5, 3, 2, 2, 7, 5, 5, 3, 2, 2, 7, 3, 2, 13, 3, 2, 3, 2, 7, 3, 2

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

OFFSET

0,1

LINKS

Iain Fox, Table of n, a(n) for n = 0..20000

FORMULA

a(-n) = A290838(n+1). - Iain Fox, Dec 14 2017

MATHEMATICA

Table[j=0; found=False; While[!found, j++; found=PrimeQ[2Prime[j]+2n-1]]; Prime[j], {n, 85}]

PROG

(PARI) a(n) = {my(p=2); while(!isprime(2*p+2*n-1), p = nextprime(p+1)); p; } \\ Michel Marcus, Aug 12 2017

CROSSREFS

Cf. A005384, A023204, A023205, A023206, A023207, A171517, A020483, A290838.

Cf. A067076 (indices n at which a(n) = 2).

KEYWORD

nonn,easy

AUTHOR

XU Pingya, Aug 12 2017

EXTENSIONS

a(0) prepended by Iain Fox, Dec 14 2017

STATUS

approved

A171518

Primes p such that 3*p-+8 are primes.

+10
1

5, 7, 13, 17, 53, 73, 83, 113, 127, 157, 193, 223, 277, 347, 367, 433, 613, 647, 673, 743, 797, 907, 937, 1117, 1217, 1373, 1427, 1483, 1543, 1597, 1637, 1667, 1877, 1933, 2027, 2237, 2297, 2447, 2647, 2687, 2843, 3083, 3137, 3613, 3797, 4073, 4463, 4483

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

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

EXAMPLE

5 is in the sequence since 3*5-8=7 and 3*5+8=23 are primes.

MATHEMATICA

Select[Prime[Range[7! ]], PrimeQ[3*#-8]&&PrimeQ[3*#+8]&]

CROSSREFS

Cf. A000040, A005382, A005384, A023204-A023207, A063908-A063912, A103803, A124098, A125272, A171517

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

STATUS

approved

A248372

Numbers m such that both p = 52*m + 1 and q = 52*p + 1 are prime.

+10
1

36, 39, 60, 126, 171, 189, 195, 300, 315, 405, 420, 435, 504, 540, 570, 606, 720, 756, 816, 876, 960, 1089, 1221, 1224, 1260, 1329, 1365, 1371, 1389, 1404, 1530, 1554, 1674, 1740, 1785, 1791, 1914, 1959, 2085, 2244, 2304, 2334, 2376, 2451, 2454, 2520, 2631, 2646, 2715, 2799, 2976

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

OFFSET

1,1

COMMENTS

All terms are divisible by 3, because if m == 1 or 2 (mod 3), either q or p is divisible by 3.

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

MATHEMATICA

s={}; Do[If[PrimeQ[p=52*n+1)]&&PrimeQ[52*p+1], AppendTo[s, n]], {n, 3000}]; s

PROG

(PARI)

for(n=1, 10^4, p=52*n+1; if(isprime(p)&&isprime(52*p+1), print1(n, ", "))) \\ Derek Orr, Oct 06 2014

CROSSREFS

Subsequence of A248221.

Cf. A033210, A142508, A171517, A248221, A248368.

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 05 2014

STATUS

approved

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