cp's OEIS Frontend

A190639 Centuries whose prime pattern repeats in the next century.

%I A190639 #31 Nov 12 2019 09:24:34
%S A190639 473267,726760,1773439,1808828,1919128,2131583,2165420,2339971,
%T A190639 2390652,2518488,2802591,2844914,2982584,2996184,3183263,3193175,
%U A190639 3250986,3418185,3428241,3633472,3909324,3953449,4280455,4303819,4373399,4658285,4728653,4978360,5165402,5254365
%N A190639 Centuries whose prime pattern repeats in the next century.
%C A190639 Alternate definition: Numbers x such that for all N in [100x,100x+99], N is prime iff N+100 is prime.
%C A190639 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.
%C A190639 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
%H A190639 Donovan Johnson, <a href="/A190639/b190639.txt">Table of n, a(n) for n = 1..1000</a>
%H A190639 J. K. Andersen, in reply to R. Wood, <a href="http://groups.yahoo.com/group/primenumbers/message/22717">Re: First repetition of prime pattern within "centuries"</a>, Yahoo group "primenumbers", May 15, 2011.
%H A190639 Jens Kruse Andersen, Phil Carmody, Maximilian Hasler, <a href="/A190639/a190639.txt">First repetition of prime pattern within "centuries"</a>, digest of 11 messages in primenumbers Yahoo group, May 15, 2011.
%F A190639 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
%F A190639 a(n) = A219996(n) - 1. - _V. Raman_, Dec 09 2012
%e A190639 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.
%Y A190639 Cf. A181098.
%Y A190639 Cf. A219996 (upper century).
%K A190639 nonn,base
%O A190639 1,1
%A A190639 _M. F. Hasler_, May 15 2011
%E A190639 a(1)-a(5) computed by J. K. Andersen, May 15 2011
%E A190639 a(6)-a(30) from _Donovan Johnson_, May 15 2011