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

Offset: 1

Author

Gus Wiseman, May 14 2024

Keywords

• nonn
• base

Comments

The unsorted version is A372517.

Examples

			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.
		

Links

• Wikipedia, Hamming weight.

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.

Programs

Mathematica

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

Formula

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

Extensions

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