A182381 Carmichael numbers divisible by 17 and 29.

2465, 278545, 13696033, 75151441, 93869665, 169570801, 490099681, 612347905, 707926801, 744866305, 1190790721, 1321983937, 1913016001, 2159003281, 2176838049, 2232385345, 2353639681, 3880251649, 4059151489, 4314912001, 5204110465, 8355729313, 8548543585, 9584174881, 10054063041, 10933377841

Offset

1,1

Comments

Conjecture: Any Carmichael number C divisible by 17 and 29 can be written as C = 952*n + 561; checked up to the Carmichael number 105823343809.

Note: the number 561 is the first Carmichael number and the number 952 comes from the following interesting relation: 952^2 = 1105^2 - 561^2 (where 1105 is the second Carmichael number).

The conjecture follows from Korselt's criterion. More is true: a(n) = 2465 mod 55216. - Charles R Greathouse IV, Oct 02 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

E. W. Weisstein, Carmichael Number

Prog

(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
list(lim)=my(v=List()); forstep(n=2465, lim, 55216, if(Korselt(n), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jun 30 2017

Crossrefs

Sequence in context: A152497 A365022 A329240 * A284089 A252113 A102689

Adjacent sequences: A182378 A182379 A182380 * A182382 A182383 A182384

Keyword

nonn

Author

Marius Coman, Apr 27 2012

Extensions

Terms corrected by Charles R Greathouse IV, Oct 02 2012

Status

approved