cp's OEIS Frontend

A372440 Numbers k such that the least binary index of k plus the least prime index of k is even.

%I A372440 #6 May 07 2024 20:12:35
%S A372440 4,5,11,12,16,17,20,23,25,28,31,35,36,41,44,47,48,52,55,59,60,64,65,
%T A372440 67,68,73,76,80,83,84,85,92,95,97,100,103,108,109,112,115,116,121,124,
%U A372440 125,127,132,137,140,143,144,145,148,149,155,156,157,164,167,172
%N A372440 Numbers k such that the least binary index of k plus the least prime index of k is even.
%C A372440 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 A372440 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 A372440 The terms (center), their binary indices (left), and their prime indices (right) begin:
%e A372440           {3}   4  (1,1)
%e A372440         {1,3}   5  (3)
%e A372440       {1,2,4}  11  (5)
%e A372440         {3,4}  12  (2,1,1)
%e A372440           {5}  16  (1,1,1,1)
%e A372440         {1,5}  17  (7)
%e A372440         {3,5}  20  (3,1,1)
%e A372440     {1,2,3,5}  23  (9)
%e A372440       {1,4,5}  25  (3,3)
%e A372440       {3,4,5}  28  (4,1,1)
%e A372440   {1,2,3,4,5}  31  (11)
%e A372440       {1,2,6}  35  (4,3)
%e A372440         {3,6}  36  (2,2,1,1)
%e A372440       {1,4,6}  41  (13)
%e A372440       {3,4,6}  44  (5,1,1)
%e A372440   {1,2,3,4,6}  47  (15)
%e A372440         {5,6}  48  (2,1,1,1,1)
%e A372440       {3,5,6}  52  (6,1,1)
%e A372440   {1,2,3,5,6}  55  (5,3)
%e A372440   {1,2,4,5,6}  59  (17)
%e A372440     {3,4,5,6}  60  (3,2,1,1)
%e A372440           {7}  64  (1,1,1,1,1,1)
%t A372440 bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A372440 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A372440 Select[Range[100],EvenQ[Min[bix[#]]+Min[prix[#]]]&]
%Y A372440 For sum (A372428, zeros A372427) we have A372587, complement A372586.
%Y A372440 Positions of even terms in A372437.
%Y A372440 The complement is 1 followed by A372439.
%Y A372440 For length (A372441, zeros A071814) we have A372591, complement A372590.
%Y A372440 For maximum (A372442, zeros A372436) we have A372589, complement A372588.
%Y A372440 A003963 gives product of prime indices, binary A096111.
%Y A372440 A019565 gives Heinz number of binary indices, adjoint A048675.
%Y A372440 A029837 gives greatest binary index, least A001511.
%Y A372440 A048793 lists binary indices, length A000120, reverse A272020, sum A029931.
%Y A372440 A061395 gives greatest prime index, least A055396.
%Y A372440 A070939 gives length of binary expansion.
%Y A372440 A112798 lists prime indices, length A001222, reverse A296150, sum A056239.
%Y A372440 Cf. A000720, A061712, A174090, A243055, A359402, A359495, A372429, A372430, A372431, A372432, A372438, A372471.
%K A372440 nonn,base
%O A372440 1,1
%A A372440 _Gus Wiseman_, May 06 2024