cp's OEIS Frontend

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

%I A372886 #12 Jun 20 2025 10:46:59
%S A372886 1,2,5,9,10,13,14,18,20,22,24,26,27,30,32,33,35,36,38,42,43,45,47,52,
%T A372886 57,58,60,62,63,67,70,71,74,76,79,84,88,94,96,97,99,100,101,108,116,
%U A372886 124,126,127,132,133,135,137,144,150,154,156,160,161,162,164,172
%N A372886 Indices of prime numbers whose binary indices (positions of ones in reversed binary expansion) sum to another prime number.
%C A372886 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.
%C A372886 The prime numbers themselves are A372885(n).
%H A372886 Robert Israel, <a href="/A372886/b372886.txt">Table of n, a(n) for n = 1..10000</a>
%e A372886 The binary indices of 89 = prime(24) are {1,4,5,7}, with sum 17, which is prime, so 24 is in the sequence.
%p A372886 filter:= proc(p)
%p A372886   local L,i,t;
%p A372886   L:= convert(p,base,2);
%p A372886   isprime(add(i*L[i],i=1..nops(L)))
%p A372886 end proc:
%p A372886 select(t -> filter(ithprime(t)), [$1..1000]); # _Robert Israel_, Jun 19 2025
%t A372886 Select[Range[100],PrimeQ[Total[First /@ Position[Reverse[IntegerDigits[Prime[#],2]],1]]]&]
%Y A372886 Numbers k such that A029931(prime(k)) is prime.
%Y A372886 Indices of primes that belong to A372689.
%Y A372886 The indexed prime numbers themselves are A372885.
%Y A372886 A000040 lists the prime numbers, A014499 their binary indices
%Y A372886 A006450 lists primes of prime index, prime case of A316091.
%Y A372886 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372886 A038499 counts partitions of prime length, strict A085756.
%Y A372886 Binary indices:
%Y A372886 - listed A048793, sum A029931
%Y A372886 - reversed A272020
%Y A372886 - opposite A371572, sum A230877
%Y A372886 - length A000120, complement A023416
%Y A372886 - min A001511, opposite A000012
%Y A372886 - max A070939, opposite A070940
%Y A372886 - complement A368494, sum A359400
%Y A372886 - opposite complement A371571, sum A359359
%Y A372886 A058698 counts partitions of prime numbers, strict A064688.
%Y A372886 A372687 counts strict partitions of prime binary rank, counted by A372851.
%Y A372886 A372688 counts partitions of prime binary rank, with Heinz numbers A277319.
%Y A372886 Cf. A029837, A158704, A158705, A035100, A372429, A372471, A372850.
%K A372886 nonn,base
%O A372886 1,2
%A A372886 _Gus Wiseman_, May 19 2024