cp's OEIS Frontend

A371444 Numbers whose binary indices are composite numbers.

%I A371444 #5 Mar 30 2024 15:59:44
%S A371444 8,32,40,128,136,160,168,256,264,288,296,384,392,416,424,512,520,544,
%T A371444 552,640,648,672,680,768,776,800,808,896,904,928,936,2048,2056,2080,
%U A371444 2088,2176,2184,2208,2216,2304,2312,2336,2344,2432,2440,2464,2472,2560,2568
%N A371444 Numbers whose binary indices are composite numbers.
%C A371444 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.
%e A371444 The terms together with their binary expansions and binary indices begin:
%e A371444      8:           1000 ~ {4}
%e A371444     32:         100000 ~ {6}
%e A371444     40:         101000 ~ {4,6}
%e A371444    128:       10000000 ~ {8}
%e A371444    136:       10001000 ~ {4,8}
%e A371444    160:       10100000 ~ {6,8}
%e A371444    168:       10101000 ~ {4,6,8}
%e A371444    256:      100000000 ~ {9}
%e A371444    264:      100001000 ~ {4,9}
%e A371444    288:      100100000 ~ {6,9}
%e A371444    296:      100101000 ~ {4,6,9}
%e A371444    384:      110000000 ~ {8,9}
%e A371444    392:      110001000 ~ {4,8,9}
%e A371444    416:      110100000 ~ {6,8,9}
%e A371444    424:      110101000 ~ {4,6,8,9}
%e A371444    512:     1000000000 ~ {10}
%e A371444    520:     1000001000 ~ {4,10}
%e A371444    544:     1000100000 ~ {6,10}
%e A371444    552:     1000101000 ~ {4,6,10}
%e A371444    640:     1010000000 ~ {8,10}
%e A371444    648:     1010001000 ~ {4,8,10}
%e A371444    672:     1010100000 ~ {6,8,10}
%t A371444 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A371444 Select[Range[100],EvenQ[#]&&And@@Not/@PrimeQ/@bpe[#]&]
%Y A371444 For powers of 2 instead of composite numbers we have A253317.
%Y A371444 For prime indices we have the even case of A320628.
%Y A371444 For prime instead of composite we have A326782.
%Y A371444 This is the even case of A371444.
%Y A371444 An opposite version is A371449.
%Y A371444 A000040 lists prime numbers, complement A018252.
%Y A371444 A000961 lists prime-powers.
%Y A371444 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A371444 A070939 gives length of binary expansion.
%Y A371444 A096111 gives product of binary indices.
%Y A371444 Cf. A001222, A005117, A055887, A320629, A326781, A368109, A368533, A371289, A371452.
%K A371444 nonn
%O A371444 1,1
%A A371444 _Gus Wiseman_, Mar 30 2024