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

Author

Reinhard Zumkeller, Aug 07 2010

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A014499, A004676.

Programs

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 *)

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