A371443 - OEIS

%I #6 Mar 30 2024 15:59:53

%S 1,8,9,32,33,40,41,128,129,136,137,160,161,168,169,256,257,264,265,

%T 288,289,296,297,384,385,392,393,416,417,424,425,512,513,520,521,544,

%U 545,552,553,640,641,648,649,672,673,680,681,768,769,776,777,800,801,808

%N Numbers whose binary indices are nonprime numbers.

%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.

%e The terms together with their binary expansions and binary indices begin:

%e     1:          1 ~ {1}

%e     8:       1000 ~ {4}

%e     9:       1001 ~ {1,4}

%e    32:     100000 ~ {6}

%e    33:     100001 ~ {1,6}

%e    40:     101000 ~ {4,6}

%e    41:     101001 ~ {1,4,6}

%e   128:   10000000 ~ {8}

%e   129:   10000001 ~ {1,8}

%e   136:   10001000 ~ {4,8}

%e   137:   10001001 ~ {1,4,8}

%e   160:   10100000 ~ {6,8}

%e   161:   10100001 ~ {1,6,8}

%e   168:   10101000 ~ {4,6,8}

%e   169:   10101001 ~ {1,4,6,8}

%e   256:  100000000 ~ {9}

%e   257:  100000001 ~ {1,9}

%e   264:  100001000 ~ {4,9}

%e   265:  100001001 ~ {1,4,9}

%e   288:  100100000 ~ {6,9}

%e   289:  100100001 ~ {1,6,9}

%e   296:  100101000 ~ {4,6,9}

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t Select[Range[100],And@@Not/@PrimeQ/@bpe[#]&]

%Y For powers of 2 instead of nonprime numbers we have A253317.

%Y For prime indices instead of binary indices we have A320628.

%Y For prime instead of nonprime we have A326782.

%Y For composite numbers we have A371444.

%Y An opposite version is A371449.

%Y A000040 lists prime numbers, complement A018252.

%Y A000961 lists prime-powers.

%Y A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

%Y A070939 gives length of binary expansion.

%Y A096111 gives product of binary indices.

%Y Cf. A001222, A005117, A326781, A368109, A368533, A371289, A371452.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 30 2024