A139466 Smallest prime factor of n! + 2n - 1.

2, 5, 11, 31, 3, 17, 31, 3, 362897, 3628819, 3, 251, 5, 3, 93407, 200989, 3, 5, 211, 3, 199, 38189, 3, 314707, 7, 3, 2473, 5, 3, 98274048659069, 1447, 3, 5, 585341, 3, 61, 8150209692797, 3, 7, 131, 3, 193, 5, 3, 73, 7, 3, 5, 53, 3, 647, 151897, 3, 67801, 7001

Offset

1,1

Links

Apurva Rai, Table of n, a(n) for n = 1..105 (terms n = 1..60 from Amiram Eldar)

Florian Luca and Igor E. Shparlinski, On the largest prime factor of n! + 2^n - 1, Journal de Theorie des Nombres de Bordeaux 17 (2005), 859-870.

Apurva Rai, Python program to test a(61)-a(105)

Formula

a(n) = A020639(A139464(n)). - Amiram Eldar, Feb 05 2020

Mathematica

a = {}; Do[AppendTo[a, n! + 2 n - 1], {n, 1, 40}]; b = {}; Do[c = FactorInteger[a[[n]]]; d = c[[1]]; AppendTo[b, d[[1]]], {n, 1, Length[a]}]; b (* Artur Jasinski *)
FactorInteger[#][[1, 1]] & /@ Table[n! + 2*n - 1, {n, 1, 18}] (* Amiram Eldar, Feb 05 2020 ()

Prog

(PARI) a(n)=factor(n!+2*n-1)[1, 1] \\ Charles R Greathouse IV, Feb 01 2013

Crossrefs

Cf. A020639, A127986, A127987, A139023, A139024, A139464, A139465, A139467.

Sequence in context: A131347 A292210 A079225 * A291139 A139467 A124481

Adjacent sequences: A139463 A139464 A139465 * A139467 A139468 A139469

Keyword

nonn

Author

Artur Jasinski, Apr 22 2008

Extensions

a(41)-a(55) from Amiram Eldar, Feb 05 2020

Status

approved