A100723 Prime numbers whose binary representations are split into exactly seven runs.

149, 173, 181, 277, 293, 331, 337, 347, 349, 373, 421, 557, 587, 593, 599, 601, 613, 617, 619, 653, 659, 673, 691, 701, 709, 727, 733, 757, 809, 811, 821, 857, 859, 877, 937, 941, 1061, 1069, 1093, 1097, 1117, 1129, 1163, 1171, 1181, 1187, 1201, 1213

Offset

1,1

Comments

The n-th prime is a member iff A100714(n)=7

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Run-Length Encoding.

Example

a(3) = 181 is a member because it is the 3rd prime whose binary representation splits into exactly 7 runs: 181_10 = 10110101_2.

Maple

qprime:= proc(n) if isprime(n) then n fi end proc:
[seq(seq(seq(seq(seq(seq(seq(qprime(2^i1 - 2^i2 + 2^i3 - 2^i4 + 2^i5
- 2^i6 + 2^i7-1), i7 = 1..i6-1), i6=i5-1..2, -1), i5=3..i4-1),  i4=i3-1..4, -1), i3=5..i2-1), i2=i1-1..6, -1), i1=7..12)]; # Robert Israel, Nov 24 2020

Mathematica

Select[Table[Prime[k], {k, 1, 50000}], Length[Split[IntegerDigits[ #, 2]]] == 7 &]

Crossrefs

Cf. A100714, A000040.

Sequence in context: A268428 A190654 A308895 * A316589 A178127 A307472

Adjacent sequences: A100720 A100721 A100722 * A100724 A100725 A100726

Keyword

base,nonn

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004

Status

approved