A372471 Irregular triangle read by rows where row n lists the binary indices of the n-th prime number.

2, 1, 2, 1, 3, 1, 2, 3, 1, 2, 4, 1, 3, 4, 1, 5, 1, 2, 5, 1, 2, 3, 5, 1, 3, 4, 5, 1, 2, 3, 4, 5, 1, 3, 6, 1, 4, 6, 1, 2, 4, 6, 1, 2, 3, 4, 6, 1, 3, 5, 6, 1, 2, 4, 5, 6, 1, 3, 4, 5, 6, 1, 2, 7, 1, 2, 3, 7, 1, 4, 7, 1, 2, 3, 4, 7, 1, 2, 5, 7, 1, 4, 5, 7, 1, 6, 7

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.

Links

Table of n, a(n) for n=1..87.

Example

We have prime(12) = (2^1 + 2^3 + 2^6)/2, so row 12 is (1,3,6).
Each prime followed by its binary indices:
   2: 2
   3: 1 2
   5: 1 3
   7: 1 2 3
  11: 1 2 4
  13: 1 3 4
  17: 1 5
  19: 1 2 5
  23: 1 2 3 5
  29: 1 3 4 5
  31: 1 2 3 4 5
  37: 1 3 6
  41: 1 4 6
  43: 1 2 4 6
  47: 1 2 3 4 6

Mathematica

Table[Join@@Position[Reverse[IntegerDigits[Prime[n], 2]], 1], {n, 15}]

Crossrefs

Row lengths are A014499.

Second column is A023506(n) + 1.

Final column is A035100.

Prime-indexed rows of A048793.

Row-sums are A372429, restriction of A029931 (sum of binary indices).

A019565 gives Heinz number of binary indices, adjoint A048675.

A029837 gives greatest binary index, least A001511.

A048793 lists binary indices, length A000120, reverse A272020.

A070939 gives length of binary expansion.

Cf. A000040, A005940, A056239, A071814, A096111, A191232, A230877, A231204, A372427-A372442.

Sequence in context: A263274 A333940 A292997 * A060135 A057112 A071956

Adjacent sequences: A372468 A372469 A372470 * A372472 A372473 A372474

Keyword

nonn,tabf,base

Author

Gus Wiseman, May 07 2024

Status

approved