%I #45 Jan 04 2024 06:35:52
%S 2341,89101234567,45678910111213123,
%T 23456789101112131415161718192021222324251,
%U 30313233341234567891011121314151617181920212223242526272829,20212223242526272829303132333435363738394041424344454612345678910111213141516171819,42434445461234567891011121314151617181920212223242526272829303132333435363738394041,14151617181920212223242526272829303132333435363738394041424344454647484950515212345678910111213
%N Smallest primes of the form (i+1)(i+2)...(h-1)(h)1234...(i-1)(i). These elements, by definition, belong to A001292.
%C If we indicate by p(j) the j-th term of A001292, the sequence above can be synthesized as:
%C 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 The first 30 terms of the sequence contain fewer than 500 digits. Among the first 22155 terms of A001292 only 31 are primes.
%D Marco Ripà, "Rudimatematici", Bookshelf, October 2010.
%D M. Vassilev-Missana and K. Atanassov, "Some Smarandache problems", Hexis, 2004.
%H 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 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 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 Marco Ripà, <a href="http://vixra.org/abs/1101.0092">On prime factors in old and new sequences of integers</a>, vixra, 2011.
%H 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 Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, Xiquan Publ., Phoenix-Chicago, 1993.
%o (Python) # uses A001292gen() and imports from A001292
%o from sympy import isprime
%o def agen(): yield from filter(isprime, A001292gen())
%o print(list(islice(agen(), 10))) # _Michael S. Branicky_, Jul 01 2022
%Y Cf. A001292, A176942.
%K nonn,base
%O 1,1
%A _Marco Ripà_, Jan 23 2011
%E Edited by _N. J. A. Sloane_, Jan 25 2011