cp's OEIS Frontend

A372439 Numbers k such that the least binary index of k plus the least prime index of k is odd.

%I A372439 #9 May 07 2024 20:12:41
%S A372439 2,3,6,7,8,9,10,13,14,15,18,19,21,22,24,26,27,29,30,32,33,34,37,38,39,
%T A372439 40,42,43,45,46,49,50,51,53,54,56,57,58,61,62,63,66,69,70,71,72,74,75,
%U A372439 77,78,79,81,82,86,87,88,89,90,91,93,94,96,98,99,101,102
%N A372439 Numbers k such that the least binary index of k plus the least prime index of k is odd.
%C A372439 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 A372439 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 A372439 The terms (center), their binary indices (left), and their prime indices (right) begin:
%e A372439         {2}   2  (1)
%e A372439       {1,2}   3  (2)
%e A372439       {2,3}   6  (2,1)
%e A372439     {1,2,3}   7  (4)
%e A372439         {4}   8  (1,1,1)
%e A372439       {1,4}   9  (2,2)
%e A372439       {2,4}  10  (3,1)
%e A372439     {1,3,4}  13  (6)
%e A372439     {2,3,4}  14  (4,1)
%e A372439   {1,2,3,4}  15  (3,2)
%e A372439       {2,5}  18  (2,2,1)
%e A372439     {1,2,5}  19  (8)
%e A372439     {1,3,5}  21  (4,2)
%e A372439     {2,3,5}  22  (5,1)
%e A372439       {4,5}  24  (2,1,1,1)
%e A372439     {2,4,5}  26  (6,1)
%e A372439   {1,2,4,5}  27  (2,2,2)
%e A372439   {1,3,4,5}  29  (10)
%e A372439   {2,3,4,5}  30  (3,2,1)
%e A372439         {6}  32  (1,1,1,1,1)
%e A372439       {1,6}  33  (5,2)
%e A372439       {2,6}  34  (7,1)
%t A372439 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372439 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372439 Select[Range[100],OddQ[Min[bix[#]]+Min[prix[#]]]&]
%Y A372439 Positions of odd terms in A372437.
%Y A372439 The complement is 1 followed by A372440.
%Y A372439 For sum (A372428, zeros A372427) we have A372586, complement A372587.
%Y A372439 For maximum (A372442, zeros A372436) we have A372588, complement A372589.
%Y A372439 For length (A372441, zeros A071814) we have A372590, complement A372591.
%Y A372439 A003963 gives product of prime indices, binary A096111.
%Y A372439 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372439 A029837 gives greatest binary index, least A001511.
%Y A372439 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372439 A061395 gives greatest prime index, least A055396.
%Y A372439 A070939 gives length of binary expansion.
%Y A372439 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372439 Cf. A000720, A061712, A174090, A243055, A359495, A372429, A372430, A372431, A372432, A372438, A372471.
%K A372439 nonn,base
%O A372439 1,1
%A A372439 _Gus Wiseman_, May 06 2024