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A307503 Least prime containing at least n consecutive 1's in its binary representation. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)