A057713 Smallest prime divisor of Kummer numbers ( = primorials - 1), or 1 if no such prime exists.
1, 5, 29, 11, 2309, 30029, 61, 53, 37, 79, 228737, 229, 304250263527209, 141269, 191, 87337, 27600124633, 1193, 163, 260681003321, 313, 163, 139, 23768741896345550770650537601358309, 66683, 2990092035859, 15649, 17515703, 719, 295201, 15098753, 10172884549, 20962699238647, 4871, 673, 311, 1409, 1291, 331, 1450184819, 23497, 711427, 521, 673, 519577, 1372062943, 56543, 811, 182309, 53077, 641, 349, 389
Offset: 1
Keywords
Examples
6th term in the sequence corresponds to 7th primorial = 510510 and 510509 = 61 * 8369, so a(7) = 61.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..99
- M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
- R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - _N. J. A. Sloane_, Jun 13 2012
- Hisanori Mishima, Factorizations of many number sequences
- R. G. Wilson v, Explicit factorizations
Programs
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Mathematica
Map[If[PrimeQ@ #, #, FactorInteger[#][[1, 1]]] &, FoldList[#1 #2 &, Prime@ Range@ 36] - 1] (* Michael De Vlieger, Feb 18 2017 *)
Formula
Extensions
More terms from Klaus Brockhaus, Larry Reeves (larryr(AT)acm.org) and Robert G. Wilson v, Apr 02 2001