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A100723
Prime numbers whose binary representations are split into exactly seven runs.
1
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
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
Sequence in context: A268428 A190654 A308895 * A316589 A178127 A307472
KEYWORD
base,nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 11 2004
STATUS
approved