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A181129 Smallest primes of the form (i+1)(i+2)...(h-1)(h)1234...(i-1)(i). These elements, by definition, belong to A001292.

%I A181129 #45 Jan 04 2024 06:35:52
%S A181129 2341,89101234567,45678910111213123,
%T A181129 23456789101112131415161718192021222324251,
%U A181129 30313233341234567891011121314151617181920212223242526272829,20212223242526272829303132333435363738394041424344454612345678910111213141516171819,42434445461234567891011121314151617181920212223242526272829303132333435363738394041,14151617181920212223242526272829303132333435363738394041424344454647484950515212345678910111213
%N A181129 Smallest primes of the form (i+1)(i+2)...(h-1)(h)1234...(i-1)(i). These elements, by definition, belong to A001292.
%C A181129 If we indicate by p(j) the j-th term of A001292, the sequence above can be synthesized as:
%C A181129 p(8), p(53), p(82), p(302), p(591), p(1055), p(1077), p(1340), p(1499), p(1890), p(2231), p(3109), p(3145), p(3620), p(3878), p(4405), p(6248), p(8878), p(8888), p(11329), p(11439), p(12310), p(12344), p(13323), p(13747), p(15883), p(17471), p(17985), p(19815), p(20335), p(21676).
%C A181129 The first 30 terms of the sequence contain fewer than 500 digits. Among the first 22155 terms of A001292 only 31 are primes.
%D A181129 Marco Ripà, "Rudimatematici", Bookshelf, October 2010.
%D A181129 M. Vassilev-Missana and K. Atanassov, "Some Smarandache problems", Hexis, 2004.
%H A181129 Michael S. Branicky, <a href="/A181129/b181129.txt">Table of n, a(n) for n = 1..46</a> (terms 1..31 from Marco Ripà)
%H A181129 Kenichiro Kashihara, <a href="http://www.gallup.unm.edu/~smarandache/Kashihara.pdf">Comments and Topics on Smarandache Notions and Problems</a>, Erhus University Press, 1996, 50 pages.
%H A181129 Kenichiro Kashihara, <a href="/A011772/a011772.pdf">Comments and Topics on Smarandache Notions and Problems</a>, Erhus University Press, 1996, 50 pages. [Cached copy]
%H A181129 Marco Ripà, <a href="http://vixra.org/abs/1101.0092">On prime factors in old and new sequences of integers</a>, vixra, 2011.
%H A181129 Marco Ripa, <a href="http://www.nntdm.net/papers/nntdm-18/NNTDM-18-1-29-48.pdf">Patterns related to the Smarandache circular sequence primality problem</a>, Notes Numb. Th. Discr. Math., vol. 18(1) (2012), pp. 29-48.
%H A181129 Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Xiquan Publ., Phoenix-Chicago, 1993.
%o A181129 (Python) # uses A001292gen() and imports from A001292
%o A181129 from sympy import isprime
%o A181129 def agen(): yield from filter(isprime, A001292gen())
%o A181129 print(list(islice(agen(), 10))) # _Michael S. Branicky_, Jul 01 2022
%Y A181129 Cf. A001292, A176942.
%K A181129 nonn,base
%O A181129 1,1
%A A181129 _Marco Ripà_, Jan 23 2011
%E A181129 Edited by _N. J. A. Sloane_, Jan 25 2011