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

4, 5, 11, 12, 16, 17, 20, 23, 25, 28, 31, 35, 36, 41, 44, 47, 48, 52, 55, 59, 60, 64, 65, 67, 68, 73, 76, 80, 83, 84, 85, 92, 95, 97, 100, 103, 108, 109, 112, 115, 116, 121, 124, 125, 127, 132, 137, 140, 143, 144, 145, 148, 149, 155, 156, 157, 164, 167, 172

Offset

1,1

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.

Links

Table of n, a(n) for n=1..59.

Example

The terms (center), their binary indices (left), and their prime indices (right) begin:
          {3}   4  (1,1)
        {1,3}   5  (3)
      {1,2,4}  11  (5)
        {3,4}  12  (2,1,1)
          {5}  16  (1,1,1,1)
        {1,5}  17  (7)
        {3,5}  20  (3,1,1)
    {1,2,3,5}  23  (9)
      {1,4,5}  25  (3,3)
      {3,4,5}  28  (4,1,1)
  {1,2,3,4,5}  31  (11)
      {1,2,6}  35  (4,3)
        {3,6}  36  (2,2,1,1)
      {1,4,6}  41  (13)
      {3,4,6}  44  (5,1,1)
  {1,2,3,4,6}  47  (15)
        {5,6}  48  (2,1,1,1,1)
      {3,5,6}  52  (6,1,1)
  {1,2,3,5,6}  55  (5,3)
  {1,2,4,5,6}  59  (17)
    {3,4,5,6}  60  (3,2,1,1)
          {7}  64  (1,1,1,1,1,1)

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], EvenQ[Min[bix[#]]+Min[prix[#]]]&]

Crossrefs

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

Positions of even terms in A372437.

The complement is 1 followed by A372439.

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

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

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, A359402, A359495, A372429, A372430, A372431, A372432, A372438, A372471.

Sequence in context: A317304 A178823 A188053 * A261673 A027708 A047374

Adjacent sequences: A372437 A372438 A372439 * A372441 A372442 A372443

Keyword

nonn,base

Author

Gus Wiseman, May 06 2024

Status

approved