A372886 Indices of prime numbers whose binary indices (positions of ones in reversed binary expansion) sum to another prime number.

1, 2, 5, 9, 10, 13, 14, 18, 20, 22, 24, 26, 27, 30, 32, 33, 35, 36, 38, 42, 43, 45, 47, 52, 57, 58, 60, 62, 63, 67, 70, 71, 74, 76, 79, 84, 88, 94, 96, 97, 99, 100, 101, 108, 116, 124, 126, 127, 132, 133, 135, 137, 144, 150, 154, 156, 160, 161, 162, 164, 172

Offset: 1

Author

Gus Wiseman, May 19 2024

Keywords

• nonn
• base

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

The prime numbers themselves are A372885(n).

Examples

			The binary indices of 89 = prime(24) are {1,4,5,7}, with sum 17, which is prime, so 24 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers k such that A029931(prime(k)) is prime.

Indices of primes that belong to A372689.

The indexed prime numbers themselves are A372885.

A000040 lists the prime numbers, A014499 their binary indices

A006450 lists primes of prime index, prime case of A316091.

A019565 gives Heinz number of binary indices, adjoint A048675.

A038499 counts partitions of prime length, strict A085756.

Binary indices:

- listed A048793, sum A029931

- reversed A272020

- opposite A371572, sum A230877

- length A000120, complement A023416

- min A001511, opposite A000012

- max A070939, opposite A070940

- complement A368494, sum A359400

- opposite complement A371571, sum A359359

A058698 counts partitions of prime numbers, strict A064688.

A372687 counts strict partitions of prime binary rank, counted by A372851.

A372688 counts partitions of prime binary rank, with Heinz numbers A277319.

Cf. A029837, A158704, A158705, A035100, A372429, A372471, A372850.

Programs

Maple

filter:= proc(p)
  local L,i,t;
  L:= convert(p,base,2);
  isprime(add(i*L[i],i=1..nops(L)))
end proc:
select(t -> filter(ithprime(t)), [$1..1000]); # Robert Israel, Jun 19 2025

Mathematica

Select[Range[100],PrimeQ[Total[First /@ Position[Reverse[IntegerDigits[Prime[#],2]],1]]]&]