

A100726


Prime numbers whose binary representations are split into a maximum of 7 runs.


0



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
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OFFSET

1,1


COMMENTS

The nth prime is a member iff A100714(n) <= 7.
Missing primes begin 661, 677, 683, 853, 1109, 1193, 1237, 1301, 1321, 1361, 1367, 1373, ....  Charles R Greathouse IV, Oct 19 2015


LINKS

Table of n, a(n) for n=1..59.
Eric Weisstein's World of Mathematics, "RunLength Encoding."


EXAMPLE

a(3)=5 is a member because it is the 3rd prime whose binary representation splits into at most 7 runs. 5_10=101_2


MATHEMATICA

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


PROG

(PARI) is(n)=hammingweight(bitxor(n, n>>1))<8 && isprime(n) \\ Charles R Greathouse IV, Oct 19 2015


CROSSREFS

Cf. A100714, A000040.
Sequence in context: A216885 A216886 A273960 * A015919 A064555 A216887
Adjacent sequences: A100723 A100724 A100725 * A100727 A100728 A100729


KEYWORD

base,nonn


AUTHOR

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


STATUS

approved



