%I #5 May 19 2024 19:42:50
%S 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 57,58,60,62,63,67,70,71,74,76,79,84,88,94,96,97,99,100,101,108,116,
%U 124,126,127,132,133,135,137,144,150,154,156,160,161,162,164,172
%N Indices of prime numbers whose binary indices (positions of ones in reversed binary expansion) sum to another prime number.
%C 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 The prime numbers themselves are A372885(n).
%e The binary indices of 89 = prime(24) are {1,4,5,7}, with sum 17, which is prime, so 24 is in the sequence.
%t Select[Range[100],PrimeQ[Total[First /@ Position[Reverse[IntegerDigits[Prime[#],2]],1]]]&]
%Y Numbers k such that A029931(prime(k)) is prime.
%Y Indices of primes that belong to A372689.
%Y The indexed prime numbers themselves are A372885.
%Y A000040 lists the prime numbers, A014499 their binary indices
%Y A006450 lists primes of prime index, prime case of A316091.
%Y A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A038499 counts partitions of prime length, strict A085756.
%Y Binary indices:
%Y - listed A048793, sum A029931
%Y - reversed A272020
%Y - opposite A371572, sum A230877
%Y - length A000120, complement A023416
%Y - min A001511, opposite A000012
%Y - max A070939, opposite A070940
%Y - complement A368494, sum A359400
%Y - opposite complement A371571, sum A359359
%Y A058698 counts partitions of prime numbers, strict A064688.
%Y A372687 counts strict partitions of prime binary rank, counted by A372851.
%Y A372688 counts partitions of prime binary rank, with Heinz numbers A277319.
%Y Cf. A029837, A158704, A158705, A035100, A372429, A372471, A372850.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 19 2024