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A373471
Primes indices of nonzero bits in Pi (A256108).
1
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
1,1
COMMENTS
Base 2 analog of A088565 (prime positions of '1's in decimal digits of Pi).
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jul 27 2024
STATUS
approved