A090457 -id:A090457

Search: a090457 -id:a090457

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A090455

Difference between numbers of binary 1's of n and binary 1's of n-th prime.

+10
6

0, -1, 0, -2, -1, -1, 1, -2, -2, -2, -2, -1, 0, -1, -1, -3, -3, -3, 0, -2, 0, -2, 0, -2, 0, -1, -1, -2, -1, 0, -2, -2, -1, -2, -1, -3, -2, -1, -1, -3, -2, -2, -3, 0, 0, -1, 0, -5, -2, -2, -1, -4, -1, -3, 3, -1, 0, -1, 1, 0, 0, 1, 1, -5, -3, -4, -2, -2, -3, -3, 0, -4, -4, -3

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

OFFSET

1,4

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000120(n) - A014499(n);

a(A071600(n)) = a(A049084(A072439(n))) = 0.

a(A049084(A090456(n))) < 0.

a(A049084(A090457(n))) > 0.

MATHEMATICA

Table[DigitCount[n, 2, 1]-DigitCount[Prime[n], 2, 1], {n, 80}] (* Harvey P. Dale, Aug 08 2013 *)

CROSSREFS

Cf. A000120, A014499.

Cf. A007088, A004676, A090431.

Cf. A049084, A071600, A090456, A090457.

KEYWORD

sign,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

EXTENSIONS

Definition clarified by Harvey P. Dale, Aug 08 2013

STATUS

approved

A090433

Primes p(k) having a smaller sum of digits than k.

+10
4

11, 13, 23, 61, 101, 103, 107, 109, 151, 163, 211, 223, 227, 241, 251, 271, 311, 313, 317, 331, 337, 347, 401, 421, 431, 433, 443, 461, 503, 509, 521, 523, 701, 911, 1009, 1013, 1021, 1031, 1033, 1051, 1061, 1063, 1103, 1109, 1117, 1123, 1129, 1151

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

OFFSET

1,1

COMMENTS

A090431(a(n)) > 0.

LINKS

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

MATHEMATICA

Select[Prime[Range[200]], Total[IntegerDigits[#]]<Total[IntegerDigits[ PrimePi[ #]]]&] (* Harvey P. Dale, Mar 05 2017 *)

CROSSREFS

Cf. A033548, A090432, A007953, A007605, A090457.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

STATUS

approved

A090456

Primes prime(k) having more binary 1's than k.

+10
4

3, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 71, 79, 89, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 199, 223, 227, 229, 233, 239, 241, 251, 263, 271, 311, 313, 317, 331, 337, 347, 349, 359, 367, 373, 379, 383

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

OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

A090455(a(n)) < 0.

MATHEMATICA

Select[Prime[Range[100]], Differences[DigitCount[{PrimePi[#], #}, 2, 1]][[1]] > 0 &] (* Amiram Eldar, Apr 23 2022 *)

CROSSREFS

Cf. A000120, A004676, A007088, A014499, A072439, A090432, A090455, A090457.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

STATUS

approved

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