A090457 -id:A090457 - cp's OEIS frontend

A090455 Difference between numbers of binary 1's of n and binary 1's of n-th prime.

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

Offset: 1

Reinhard Zumkeller, Dec 01 2003

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

Cf. A000120, A014499.
Cf. A007088, A004676, A090431.
Cf. A049084, A071600, A090456, A090457.

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

a(n) = A000120(n) - A014499(n);
a(A071600(n)) = a(A049084(A072439(n))) = 0.
a(A049084(A090456(n))) < 0.
a(A049084(A090457(n))) > 0.

Definition clarified by Harvey P. Dale, Aug 08 2013

A090433 Primes p(k) having a smaller sum of digits than k.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Dec 01 2003

A090431(a(n)) > 0.

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

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

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

A090456 Primes prime(k) having more binary 1's than k.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Dec 01 2003

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

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

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

A090455(a(n)) < 0.

cp's OEIS Frontend

A090455 Difference between numbers of binary 1's of n and binary 1's of n-th prime.

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A090433 Primes p(k) having a smaller sum of digits than k.

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Mathematica

A090456 Primes prime(k) having more binary 1's than k.

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Keywords

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Programs

Mathematica

Formula