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

2341, 89101234567, 45678910111213123, 23456789101112131415161718192021222324251, 30313233341234567891011121314151617181920212223242526272829, 20212223242526272829303132333435363738394041424344454612345678910111213141516171819, 42434445461234567891011121314151617181920212223242526272829303132333435363738394041, 14151617181920212223242526272829303132333435363738394041424344454647484950515212345678910111213

Offset

1,1

Comments

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.

References

Marco Ripà, "Rudimatematici", Bookshelf, October 2010. M. Vassilev-Missana and K. Atanassov, "Some Smarandache problems", Hexis, 2004.

Links

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 Ripà, On prime factors in old and new sequences of integers, vixra, 2011.

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.

Prog

(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

Crossrefs

Cf. A001292, A176942.

Sequence in context: A043440 A023938 A132204 * A064868 A263556 A255099

Adjacent sequences: A181126 A181127 A181128 * A181130 A181131 A181132

Keyword

nonn,base

Author

Marco Ripà, Jan 23 2011

Extensions

Edited by N. J. A. Sloane, Jan 25 2011

Status

approved