cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A307503 Least prime containing at least n consecutive 1's in its binary representation.

Original entry on oeis.org

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

Views

Author

John Mason, Apr 11 2019

Keywords

Comments

For n > 0, a(n) = A000040(m) for the lowest m such that A090000(m) >= n.
a(n) = A087522(n) for n = 0 through 7, and in all other cases when a(n) is a base 2 repunit (Mersenne) prime.

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.
		

Crossrefs

Cf. A090593 (with exactly n consecutive ones).

Programs

  • 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