A228000 Smallest prime factor of 144396166620968*n + 1.

3, 7, 5, 3, 17, 11, 3, 5, 7, 3, 29, 47, 3, 2021546332693553, 401, 3, 11, 5, 3, 1013, 31, 3, 5, 27301567, 3, 23, 419, 3, 179, 7, 3, 13, 5, 3, 61, 1093, 3, 5, 11, 3, 25665929, 757, 3, 7, 13, 3, 331, 5, 3, 11, 7, 3, 5, 3613, 3, 17, 6977, 3, 47, 349, 3, 151, 5, 3, 7

Offset

1,1

Comments

In 1951, A. Ferrier showed that every prime factor of N = (2^148 + 1)/17 is of the form 144396166620968*n + 1, n > 0. He also noted that the first 11 numbers of this form have prime factors under 30 and hence cannot be primes, which implies that N is prime.

References

Hans Riesel, Prime numbers and computer methods for factorization, Springer, New York, 2012, pp. 122-123.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Ferrier's Prime

Mathematica

FactorInteger[#][[1, 1]]&/@(144396166620968*Range[70]+1) (* Harvey P. Dale, Oct 24 2017 *)

Prog

(PARI) for(n=1, 65, print1(factor(144396166620968*n+1)[1, 1], ", "));
(Python)
from sympy import factorint
def A228000(n):
    return min(factorint(144396166620968*n + 1)) # Chai Wah Wu, Jul 16 2019

Crossrefs

Sequence in context: A331632 A094124 A141519 * A029946 A200285 A205528

Adjacent sequences: A227997 A227998 A227999 * A228001 A228002 A228003

Keyword

nonn

Author

Arkadiusz Wesolowski, Oct 25 2013

Status

approved