cp's OEIS Frontend

A372442 (Greatest binary index of n) minus (greatest prime index of n).

%I A372442 #6 May 10 2024 08:50:29
%S A372442 1,0,2,0,1,-1,3,2,1,-1,2,-2,0,1,4,-2,3,-3,2,1,0,-4,3,2,-1,3,1,-5,2,-6,
%T A372442 5,1,-1,2,4,-6,-2,0,3,-7,2,-8,1,3,-3,-9,4,2,3,-1,0,-10,4,1,2,-2,-4,
%U A372442 -11,3,-12,-5,2,6,1,2,-12,0,-2,3,-13,5,-14,-5,4,-1
%N A372442 (Greatest binary index of n) minus (greatest prime index of n).
%C A372442 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 A372442 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.
%F A372442 a(n) = A070939(n) - A061395(n) = A029837(n) - A061395(n) for n > 1.
%t A372442 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372442 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372442 Table[Max[bix[n]]-Max[prix[n]],{n,2,100}]
%Y A372442 For sum instead of maximum we have A372428, zeros A372427.
%Y A372442 Positions of zeros are A372436.
%Y A372442 For minimum instead of maximum we have A372437, zeros {}.
%Y A372442 For length instead of maximum we have A372441, zeros A071814.
%Y A372442 Positions of odd terms are A372588, even A372589.
%Y A372442 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372442 A029837 gives greatest binary index, least A001511.
%Y A372442 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372442 A061395 gives greatest prime index, least A055396.
%Y A372442 A070939 gives length of binary expansion.
%Y A372442 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372442 Cf. A000720, A003963, A014499, A174090, A243055, A355536, A359495, A372429-A372432, A372589-A372591.
%K A372442 sign,base
%O A372442 2,3
%A A372442 _Gus Wiseman_, May 07 2024