A373471 Primes indices of nonzero bits in Pi (A256108).

3, 11, 13, 19, 23, 29, 41, 43, 47, 53, 71, 103, 107, 131, 149, 163, 173, 179, 197, 211, 227, 229, 239, 269, 281, 283, 293, 311, 349, 373, 379, 397, 409, 421, 457, 541, 557, 563, 577, 587, 599, 601, 607, 613, 617, 643, 647, 653, 659, 673, 709, 727, 733, 739, 743

Offset: 1

Author

M. F. Hasler, Jul 27 2024

Keywords

• nonn
• base

Comments

Base 2 analog of A088565 (prime positions of '1's in decimal digits of Pi).

Examples

			Written in binary, Pi = 11.0010010000111111011010101000100010...[2] = Sum_{n >= -1} 2^-A256108(n), so the bits 1 have positions (-1, 0, 3, 6, 11, 12, 13, 14, 15, 16, 18, 19, 21, 23, 25, 29, 33, ...) and primes in this sequence are (3, 11, 13, 19, 23, ...) = this sequence.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A256108 (indices of nonzero bits in Pi), A004601 (Pi in base 2), A051480 (run lengths in A004601).

Cf. A088563 (indices of '0's in decimals of Pi).

Cf. A088565 (prime indices of '1's in the decimal digits of Pi).

Programs

Mathematica

Select[PositionIndex[First[RealDigits[Pi, 2, 1000]]][1] - 2, PrimeQ] (* Paolo Xausa, Jul 31 2024 *)

PARI

select(isprime, A256108_upto(777))