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

Author

Marco Ripà, Jan 23 2011

Keywords

• nonn
• base

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.

Crossrefs

Cf. A001292, A176942.

Programs

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

Extensions

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