A373471 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

PROG

(PARI) select(isprime, A256108_upto(777))

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).

Sequence in context: A045428 A338445 A191049 * A103835 A067386 A063621

Adjacent sequences: A373468 A373469 A373470 * A373472 A373473 A373474

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Jul 27 2024

STATUS

approved