cp's OEIS Frontend

A371443 Numbers whose binary indices are nonprime numbers.

%I A371443 #6 Mar 30 2024 15:59:53
%S A371443 1,8,9,32,33,40,41,128,129,136,137,160,161,168,169,256,257,264,265,
%T A371443 288,289,296,297,384,385,392,393,416,417,424,425,512,513,520,521,544,
%U A371443 545,552,553,640,641,648,649,672,673,680,681,768,769,776,777,800,801,808
%N A371443 Numbers whose binary indices are nonprime numbers.
%C A371443 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 A371443 The terms together with their binary expansions and binary indices begin:
%e A371443     1:          1 ~ {1}
%e A371443     8:       1000 ~ {4}
%e A371443     9:       1001 ~ {1,4}
%e A371443    32:     100000 ~ {6}
%e A371443    33:     100001 ~ {1,6}
%e A371443    40:     101000 ~ {4,6}
%e A371443    41:     101001 ~ {1,4,6}
%e A371443   128:   10000000 ~ {8}
%e A371443   129:   10000001 ~ {1,8}
%e A371443   136:   10001000 ~ {4,8}
%e A371443   137:   10001001 ~ {1,4,8}
%e A371443   160:   10100000 ~ {6,8}
%e A371443   161:   10100001 ~ {1,6,8}
%e A371443   168:   10101000 ~ {4,6,8}
%e A371443   169:   10101001 ~ {1,4,6,8}
%e A371443   256:  100000000 ~ {9}
%e A371443   257:  100000001 ~ {1,9}
%e A371443   264:  100001000 ~ {4,9}
%e A371443   265:  100001001 ~ {1,4,9}
%e A371443   288:  100100000 ~ {6,9}
%e A371443   289:  100100001 ~ {1,6,9}
%e A371443   296:  100101000 ~ {4,6,9}
%t A371443 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A371443 Select[Range[100],And@@Not/@PrimeQ/@bpe[#]&]
%Y A371443 For powers of 2 instead of nonprime numbers we have A253317.
%Y A371443 For prime indices instead of binary indices we have A320628.
%Y A371443 For prime instead of nonprime we have A326782.
%Y A371443 For composite numbers we have A371444.
%Y A371443 An opposite version is A371449.
%Y A371443 A000040 lists prime numbers, complement A018252.
%Y A371443 A000961 lists prime-powers.
%Y A371443 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A371443 A070939 gives length of binary expansion.
%Y A371443 A096111 gives product of binary indices.
%Y A371443 Cf. A001222, A005117, A326781, A368109, A368533, A371289, A371452.
%K A371443 nonn
%O A371443 1,2
%A A371443 _Gus Wiseman_, Mar 30 2024