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

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, 40, 42, 43, 45, 46, 49, 50, 51, 53, 54, 56, 57, 58, 61, 62, 63, 66, 69, 70, 71, 72, 74, 75, 77, 78, 79, 81, 82, 86, 87, 88, 89, 90, 91, 93, 94, 96, 98, 99, 101, 102

Offset: 1

Author

Gus Wiseman, May 06 2024

Keywords

• nonn
• base

Comments

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.

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.

Examples

			The terms (center), their binary indices (left), and their prime indices (right) begin:
        {2}   2  (1)
      {1,2}   3  (2)
      {2,3}   6  (2,1)
    {1,2,3}   7  (4)
        {4}   8  (1,1,1)
      {1,4}   9  (2,2)
      {2,4}  10  (3,1)
    {1,3,4}  13  (6)
    {2,3,4}  14  (4,1)
  {1,2,3,4}  15  (3,2)
      {2,5}  18  (2,2,1)
    {1,2,5}  19  (8)
    {1,3,5}  21  (4,2)
    {2,3,5}  22  (5,1)
      {4,5}  24  (2,1,1,1)
    {2,4,5}  26  (6,1)
  {1,2,4,5}  27  (2,2,2)
  {1,3,4,5}  29  (10)
  {2,3,4,5}  30  (3,2,1)
        {6}  32  (1,1,1,1,1)
      {1,6}  33  (5,2)
      {2,6}  34  (7,1)
		

Crossrefs

Positions of odd terms in A372437.

The complement is 1 followed by A372440.

For sum (A372428, zeros A372427) we have A372586, complement A372587.

For maximum (A372442, zeros A372436) we have A372588, complement A372589.

For length (A372441, zeros A071814) we have A372590, complement A372591.

A003963 gives product of prime indices, binary A096111.

A019565 gives Heinz number of binary indices, adjoint A048675.

A029837 gives greatest binary index, least A001511.

A048793 lists binary indices, length A000120, reverse A272020, sum A029931.

A061395 gives greatest prime index, least A055396.

A070939 gives length of binary expansion.

A112798 lists prime indices, length A001222, reverse A296150, sum A056239.

Cf. A000720, A061712, A174090, A243055, A359495, A372429, A372430, A372431, A372432, A372438, A372471.

Programs

Mathematica

bix[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],OddQ[Min[bix[#]]+Min[prix[#]]]&]