cp's OEIS Frontend

A372437 (Least binary index of n) minus (least prime index of n).

%I A372437 #9 May 07 2024 17:41:08
%S A372437 1,-1,2,-2,1,-3,3,-1,1,-4,2,-5,1,-1,4,-6,1,-7,2,-1,1,-8,3,-2,1,-1,2,
%T A372437 -9,1,-10,5,-1,1,-2,2,-11,1,-1,3,-12,1,-13,2,-1,1,-14,4,-3,1,-1,2,-15,
%U A372437 1,-2,3,-1,1,-16,2,-17,1,-1,6,-2,1,-18,2,-1,1,-19,3
%N A372437 (Least binary index of n) minus (least prime index of n).
%C A372437 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 A372437 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.
%C A372437 Is 0 the only integer not appearing in the data?
%F A372437 a(2n) = A001511(n).
%F A372437 a(2n + 1) = -A038802(n).
%F A372437 a(n) = A001511(n) - A055396(n).
%t A372437 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372437 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372437 Table[Min[bix[n]]-Min[prix[n]],{n,2,100}]
%Y A372437 Positions of first appearances are A174090.
%Y A372437 For sum instead of minimum we have A372428, zeros A372427.
%Y A372437 For maximum instead of minimum we have A372442, zeros A372436.
%Y A372437 For length instead of minimum we have A372441, zeros A071814.
%Y A372437 A003963 gives product of prime indices.
%Y A372437 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372437 A029837 gives greatest binary index, least A001511.
%Y A372437 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372437 A061395 gives greatest prime index, least A055396.
%Y A372437 A070939 gives length of binary expansion.
%Y A372437 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372437 Cf. A000720, A014499, A061712, A243055, A304818, A355536, A359495, A359402, A372429-A372432, A372588-A372591.
%K A372437 sign,base
%O A372437 2,3
%A A372437 _Gus Wiseman_, May 06 2024