A307503 Least prime containing at least n consecutive 1's in its binary representation.
2, 2, 3, 7, 31, 31, 127, 127, 1021, 3583, 4093, 6143, 8191, 8191, 81919, 131071, 131071, 131071, 524287, 524287, 4194301, 14680063, 16777213, 67108859, 536870909, 536870909, 536870909, 536870909, 2147483647, 2147483647, 2147483647, 2147483647, 21474836479
Offset: 0
Examples
a(0) = 2, the smallest prime containing >= 0 1's. a(1) = 2, the smallest prime containing >= 1 consecutive 1's. a(2) = 3, the smallest prime containing >= 2 consecutive 1's.
Links
- Chai Wah Wu, Table of n, a(n) for n = 0..3314
Programs
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PARI
nbo(n)=if (n==0, return (0)); n>>=valuation(n, 2); if(n<2, return(n)); my(e=valuation(n+1, 2)); max(e, nbo(n>>e)); \\ A038374 a(n) = my(p=2); while(nbo(p) < n, p=nextprime(p+1)); p; \\ Michel Marcus, Apr 14 2019
Formula
a(n) <= A201914(n). - Rémy Sigrist, Apr 11 2019
a(n) = min_{k>=n} A090593(k). - Chai Wah Wu, Apr 26 2019
Extensions
a(28)-a(32) from Chai Wah Wu, Apr 26 2019
Comments