A180024 Smallest prime greater than n-th prime having as many ones in binary representation.

5, 17, 11, 13, 19, 257, 37, 29, 43, 47, 41, 67, 53, 59, 71, 61, 79, 73, 83, 97, 103, 89, 101, 131, 113, 107, 109, 151, 139, 191, 137, 193, 149, 163, 157, 167, 197, 173, 179, 181, 199, 223, 521, 263, 211, 227, 239, 229, 233, 241, 251, 271, 367, 65537, 269, 277, 283

Offset

2,1

Comments

a(n)>A000040(n) and A010051(a(n))=1 and A000120(a(n))=A000120(A000040(n));

A019434(n+1) = a(A019434(n));

If A000040(6543)=A019434(5)=65537 is the last Fermat prime, the sequence is finite with last term a(6542)=73471.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 2..6542

Example

n=10: prime(10) = 29->11101 with 4 ones,
a(10) = prime(14) = 43->101011;
n=100: prime(100) = 541->1000011101 with 5 ones,
a(100) = prime(102) = 557->1000101101;
n=1000: prime(1000) = 7919->1111011101111 with 11 ones,
a(1000) = prime(1001) = 7927->1111011110111;
n=6542: prime(6542) = 65521->1111111111110001 with 13 ones,
a(6542) = prime(7255) = 73471->10001111011111111;
n=6543: prime(6543) = 65537->10000000000000001 with 2 ones,
a(6543) = unknown.

Mathematica

sp1b[n_]:=Module[{o=DigitCount[n, 2, 1], p=NextPrime[n]}, While[ DigitCount[ p, 2, 1]!=o, p = NextPrime[ p]]; p]; sp1b/@Prime[Range[2, 60]] (* Harvey P. Dale, May 02 2019 *)

Prog

(PARI) a(n) = my(p=prime(n), x=hammingweight(p), q=nextprime(p+1)); while (hammingweight(q) != x, q=nextprime(q+1)); q; \\ Michel Marcus, Nov 12 2023

Crossrefs

Cf. A014499, A004676.

Sequence in context: A156323 A286816 A276831 * A356403 A178197 A302159

Adjacent sequences: A180021 A180022 A180023 * A180025 A180026 A180027

Keyword

nonn

Author

Reinhard Zumkeller, Aug 07 2010

Status

approved