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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. 3
2341, 89101234567, 45678910111213123, 23456789101112131415161718192021222324251, 30313233341234567891011121314151617181920212223242526272829, 20212223242526272829303132333435363738394041424344454612345678910111213141516171819, 42434445461234567891011121314151617181920212223242526272829303132333435363738394041, 14151617181920212223242526272829303132333435363738394041424344454647484950515212345678910111213 (list; graph; refs; listen; history; text; internal format)
If we indicate by p(j) the j-th term of A001292, the sequence above can be synthesized as:
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).
The first 30 terms of the sequence contain fewer than 500 digits. Among the first 22155 terms of A001292 only 31 are primes.
Marco Ripà, "Rudimatematici", Bookshelf, October 2010.
M. Vassilev-Missana and K. Atanassov, "Some Smarandache problems", Hexis, 2004.
Michael S. Branicky, Table of n, a(n) for n = 1..46 (terms 1..31 from Marco Ripà)
Kenichiro Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages.
Kenichiro Kashihara, Comments and Topics on Smarandache Notions and Problems, Erhus University Press, 1996, 50 pages. [Cached copy]
Marco Ripa, Patterns related to the Smarandache circular sequence primality problem, Notes Numb. Th. Discr. Math., vol. 18(1) (2012), pp. 29-48.
Florentin Smarandache, Only Problems, Not Solutions!, Xiquan Publ., Phoenix-Chicago, 1993.
(Python) # uses A001292gen() and imports from A001292
from sympy import isprime
def agen(): yield from filter(isprime, A001292gen())
print(list(islice(agen(), 10))) # Michael S. Branicky, Jul 01 2022
Sequence in context: A043440 A023938 A132204 * A064868 A263556 A255099
Marco Ripà, Jan 23 2011
Edited by N. J. A. Sloane, Jan 25 2011

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Last modified June 22 02:17 EDT 2024. Contains 373561 sequences. (Running on oeis4.)