A181458 Numbers n such that 41 is the largest prime factor of n^2 - 1.

40, 81, 83, 122, 124, 163, 204, 206, 247, 286, 288, 329, 409, 491, 493, 573, 575, 737, 739, 778, 901, 944, 985, 1024, 1065, 1106, 1149, 1231, 1393, 1518, 1559, 1639, 1682, 2049, 2051, 2092, 2295, 2377, 2379, 2623, 2705, 2789, 3035, 3158, 3199, 3361, 3363

Offset

1,1

Comments

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(13) = 127855050751; primepi(41) = 13.

Links

A. Jasinski, Table of n, a(n) for n = 1..262

Mathematica

jj = 2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6 *43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5; rr = {}; n = 2; While[n < 3222617400, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 41, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==41&]

Prog

(Magma) [ n: n in [2..300000] | m eq 41 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011
(Magma) p:=(97*89*83*79*73*71)^5 *(67*61*59*53*47*43*41)^6 *(37*31*29)^7 *(23*19*17)^8 *13^9 *11^10 *7^13 *5^15 *3^23 *2^36; [ n: n in [2..50000000] | p mod (n^2-1) eq 0 and (D[#D] eq 41 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 20 2011
(PARI) is(n)=n=n^2-1; forprime(p=2, 37, n/=p^valuation(n, p)); n>1 && 41^valuation(n, 41)==n \\ Charles R Greathouse IV, Jul 01 2013

Crossrefs

Cf. A175607, A181447-A181457, A181459-A181470, A181568.

Sequence in context: A037975 A317095 A039468 * A069070 A174052 A141528

Adjacent sequences: A181455 A181456 A181457 * A181459 A181460 A181461

Keyword

fini,nonn

Author

Artur Jasinski, Oct 21 2010

Status

approved