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

0,1

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 0..3314

Formula

a(n) <= A201914(n). - Rémy Sigrist, Apr 11 2019

a(n) = min_{k>=n} A090593(k). - Chai Wah Wu, Apr 26 2019

Example

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.

Prog

(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

Crossrefs

Cf. A038374, A090000, A087522, A201914.

Cf. A090593 (with exactly n consecutive ones).

Sequence in context: A038507 A077001 A180996 * A087522 A092970 A052449

Adjacent sequences: A307500 A307501 A307502 * A307504 A307505 A307506

Keyword

nonn,base

Author

John Mason, Apr 11 2019

Extensions

a(28)-a(32) from Chai Wah Wu, Apr 26 2019

Status

approved