A190639 Centuries whose prime pattern repeats in the next century.

473267, 726760, 1773439, 1808828, 1919128, 2131583, 2165420, 2339971, 2390652, 2518488, 2802591, 2844914, 2982584, 2996184, 3183263, 3193175, 3250986, 3418185, 3428241, 3633472, 3909324, 3953449, 4280455, 4303819, 4373399, 4658285, 4728653, 4978360, 5165402, 5254365

Offset

1,1

Comments

Alternate definition: Numbers x such that for all N in [100x,100x+99], N is prime iff N+100 is prime.

Contains in particular the first of two consecutive prime-free centuries, i.e., N such that there is no prime in [100 N,100 (N+2)], cf. A181098.

x belongs to this sequence if and only if the primality character of (100 * x) + k is the same as (100 * (x+1)) + k for all k = 0..99. - V. Raman, Dec 09 2012

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

J. K. Andersen, in reply to R. Wood, Re: First repetition of prime pattern within "centuries", Yahoo group "primenumbers", May 15, 2011.

Jens Kruse Andersen, Phil Carmody, Maximilian Hasler, First repetition of prime pattern within "centuries", digest of 11 messages in primenumbers Yahoo group, May 15, 2011.

Formula

a(n) ~ n. In particular there are x - 200x/log x + O(x/log^2 x) members of this sequence below x. - Charles R Greathouse IV, Dec 09 2012

a(n) = A219996(n) - 1. - V. Raman, Dec 09 2012

Example

The first value refers to two consecutive prime-free centuries (cf. A181098); the second value is such that 100*a(2)+17 and 100*a(2)+117 are the only primes between 100*a(2) and 100*(a(2)+2). See the link for more examples.

Crossrefs

Cf. A181098.

Cf. A219996 (upper century).

Sequence in context: A164973 A114673 A251370 * A228271 A219996 A183659

Adjacent sequences: A190636 A190637 A190638 * A190640 A190641 A190642

Keyword

nonn,base

Author

M. F. Hasler, May 15 2011

Extensions

a(1)-a(5) computed by J. K. Andersen, May 15 2011

a(6)-a(30) from Donovan Johnson, May 15 2011

Status

approved