A100726 - OEIS

%I #13 Jul 08 2025 06:29:55

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277

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

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

%C Missing primes begin 661, 677, 683, 853, 1109, 1193, 1237, 1301, 1321, 1361, 1367, 1373, .... - _Charles R Greathouse IV_, Oct 19 2015

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Run-LengthEncoding.html">Run-Length Encoding</a>.

%e 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.

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

%o (PARI) is(n)=hammingweight(bitxor(n, n>>1))<8 && isprime(n) \\ _Charles R Greathouse IV_, Oct 19 2015

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

%K base,nonn

%O 1,1

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