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 A226227 Numbers m such that all lengths of runs of 0's in the binary representation of m are prime numbers. 4
 1, 3, 4, 7, 8, 9, 12, 15, 17, 19, 24, 25, 28, 31, 32, 35, 36, 39, 49, 51, 56, 57, 60, 63, 65, 68, 71, 72, 73, 76, 79, 96, 99, 100, 103, 113, 115, 120, 121, 124, 127, 128, 131, 136, 137, 140, 143, 145, 147, 152, 153, 156, 159, 193, 196, 199, 200, 201, 204, 207, 224, 227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers with no 0's in base 2 (that is, 2^k - 1) are included. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 MATHEMATICA Select[Range@227, And @@ PrimeQ[(Length /@ Split@ IntegerDigits[#, 2])[[2 ;; ;; 2]]] &] (* Giovanni Resta, Jun 01 2013 *) Select[Range[250], AllTrue[Length/@Select[Split[IntegerDigits[#, 2]], MemberQ[ #, 0]&], PrimeQ]&] (* Harvey P. Dale, Aug 07 2021 *) PROG (C) #include #include typedef unsigned long long U64; U64 runs[] = {0, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43}, *wr; #define MemUSAGE 1ULL<<33 #define TOP (1ULL<<9) // <<40 ok if MemUSAGE = 1ULL<<33 int compare64(const void *p1, const void *p2) { if (*(U64*)p1 == *(U64*)p2) return 0; return (*(U64*)p1 < *(U64*)p2) ? -1 : 1; } void rec(U64 bits) { for (U64 i = 0, b; (b = bits << runs[i]) < TOP; ++i) *wr++ = b, rec(b*2+1); } int main() { U64 *wr0 = (wr = (U64*)malloc(MemUSAGE)); rec(1); //printf("%llu\n", wr-wr0); qsort(wr0, wr-wr0, 8, compare64); while (wr0

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Last modified September 8 15:58 EDT 2024. Contains 375753 sequences. (Running on oeis4.)