A100724 -id:A100724 - cp's OEIS frontend

A100726 Prime numbers whose binary representations are split into a maximum of 7 runs.

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

Offset: 1

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

The m-th prime is a term iff A100714(m) <= 7.

Missing primes begin 661, 677, 683, 853, 1109, 1193, 1237, 1301, 1321, 1361, 1367, 1373, .... - Charles R Greathouse IV, Oct 19 2015

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

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

Cf. A100714, A100725 (maximum of 5 runs), A100724 (maximum of 3 runs), A100723 (exactly 7 runs).

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

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

cp's OEIS Frontend

A100726 Prime numbers whose binary representations are split into a maximum of 7 runs.

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