A372686 - OEIS

A372686

Sorted list of positions of first appearances in A014499 (number of ones in binary expansion of each prime).

1, 2, 4, 9, 11, 31, 64, 76, 167, 309, 502, 801, 1028, 6363, 7281, 12079, 12251, 43237, 43390, 146605, 291640, 951351, 1046198, 2063216, 3957778, 11134645, 14198321, 28186247, 54387475, 105097565, 249939829, 393248783, 751545789, 1391572698, 2182112798, 8242984130

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The unsorted version is A372517.

LINKS

Table of n, a(n) for n=1..36.

Wikipedia, Hamming weight.

FORMULA

prime(a(n)) = A372685(n).

EXAMPLE

The sequence contains 9 because the first 9 terms of A014499 are 1, 2, 2, 3, 3, 3, 2, 3, 4, and the last of these is the first position of 4.

MATHEMATICA

First/@GatherBy[Range[1000], DigitCount[Prime[#], 2, 1]&]

CROSSREFS

Positions of first appearances in A014499.

The unsorted version is A372517.

For binary length we have A372684, primes A104080, firsts of A035100.

Taking primes gives A372685, unsorted version A061712.

A000120 counts ones in binary expansion (binary weight), zeros A080791.

A029837 gives greatest binary index, least A001511.

A030190 gives binary expansion, reversed A030308.

A035103 counts zeros in binary expansion of each prime, firsts A372474.

A048793 lists binary indices, reverse A272020, sum A029931.

A070939 gives length of binary expansion (number of bits).

A372471 lists binary indices of primes.

Cf. A000040, A005940, A059015, A066195, A069010, A071814, A211997, A372429, A372433, A372473, A372516.

Sequence in context: A115905 A292769 A307997 * A372517 A096134 A058885

Adjacent sequences: A372683 A372684 A372685 * A372687 A372688 A372689

KEYWORD

nonn,base

AUTHOR

Gus Wiseman, May 14 2024

EXTENSIONS

a(26)-a(36) from Pontus von Brömssen, May 15 2024

STATUS

approved