cp's OEIS Frontend

A372432 Positive integers k such that the prime indices of k are not disjoint from the binary indices of k.

%I A372432 #5 May 05 2024 08:55:31
%S A372432 3,5,6,14,15,18,20,22,27,28,30,39,42,45,51,52,54,55,56,60,63,66,68,70,
%T A372432 75,77,78,85,87,88,90,91,95,99,100,102,104,105,110,111,114,117,119,
%U A372432 121,123,125,126,133,135,138,140,147,150,152,154,159,162,165,168
%N A372432 Positive integers k such that the prime indices of k are not disjoint from the binary indices of k.
%C A372432 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 A372432 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A372432 The binary indices of 18 are {2,5}, and the prime indices are {1,2,2}, so 18 is in the sequence.
%e A372432 The terms together with their prime indices begin:
%e A372432     3: {2}
%e A372432     5: {3}
%e A372432     6: {1,2}
%e A372432    14: {1,4}
%e A372432    15: {2,3}
%e A372432    18: {1,2,2}
%e A372432    20: {1,1,3}
%e A372432    22: {1,5}
%e A372432    27: {2,2,2}
%e A372432    28: {1,1,4}
%e A372432    30: {1,2,3}
%e A372432 The terms together with their binary expansions and binary indices begin:
%e A372432     3:      11 ~ {1,2}
%e A372432     5:     101 ~ {1,3}
%e A372432     6:     110 ~ {2,3}
%e A372432    14:    1110 ~ {2,3,4}
%e A372432    15:    1111 ~ {1,2,3,4}
%e A372432    18:   10010 ~ {2,5}
%e A372432    20:   10100 ~ {3,5}
%e A372432    22:   10110 ~ {2,3,5}
%e A372432    27:   11011 ~ {1,2,4,5}
%e A372432    28:   11100 ~ {3,4,5}
%e A372432    30:   11110 ~ {2,3,4,5}
%t A372432 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372432 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372432 Select[Range[100],Intersection[bix[#],prix[#]]!={}&]
%Y A372432 For subset instead of overlap we have A372430.
%Y A372432 The complement is A372431.
%Y A372432 Equal lengths: A071814, zeros of A372441.
%Y A372432 Equal sums: A372427, zeros of A372428.
%Y A372432 Equal maxima: A372436, zeros of A372442.
%Y A372432 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372432 A029837 gives greatest binary index, least A001511.
%Y A372432 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372432 A061395 gives greatest prime index, least A055396.
%Y A372432 A070939 gives length of binary expansion.
%Y A372432 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372432 Cf. A000720, A001221, A059893, A096111, A230877, A243055, A304818, A355536, A358136, A372429.
%K A372432 nonn,base
%O A372432 1,1
%A A372432 _Gus Wiseman_, May 03 2024