

A101186


Values of k for which 7m+1, 8m+1 and 11m+1 are prime, with m = 1848k + 942.


3



13, 123, 218, 223, 278, 411, 513, 551, 588, 733, 743, 796, 856, 928, 1168, 1226, 1263, 1401, 1533, 1976, 1981, 2013, 2096, 2138, 2241, 2376, 2556, 2676, 2703, 3626, 3703, 3718, 3971, 4008, 4121, 4138, 4163, 4188, 4211, 4313, 4423, 4653, 4656, 4901, 5018
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OFFSET

1,1


COMMENTS

The number (7m+1)(8m+1)(11m+1) is a 3factor Carmichael number if and only if m is equal to 1848k+942 with k in this sequence. The sequence includes the value k = 10^329  4624879 which yields a 1000digit Carmichael number with three prime factors of 334 digits each. Other Carmichael numbers of the same form would necessarily have 4 prime factors or more; the smallest such example is 3664585=127*(7*29)*199, for m=18.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
G. P. Michon, Generic Carmichael Numbers.


EXAMPLE

a(1)=13 because k=13 corresponds to m=24966, which yields a product of three primes (7m+1)(8m+1)(11m+1) equal to the Carmichael number 9585921133193329. (Among all Carmichael numbers with 16 or fewer digits, as first listed by Richard G. E. Pinch, this one features the largest "least prime factor".)


MAPLE

filter:= proc(n) local m;
m:= 1848*n+942;
andmap(isprime, [7*m+1, 8*m+1, 11*m+1])
end proc:
select(filter, [$1..10000]); # Robert Israel, May 14 2019


PROG

(MAGMA) [k:k in [1..5100] forall{s:s in [7, 8, 11]IsPrime(m*s+1) where m is 1848*k+942}]; // Marius A. Burtea, Nov 01 2019


CROSSREFS

Cf. A002997 (Carmichael numbers), A046025.
Sequence in context: A327961 A278276 A201382 * A295778 A115204 A016277
Adjacent sequences: A101183 A101184 A101185 * A101187 A101188 A101189


KEYWORD

nonn


AUTHOR

Gerard P. Michon, Dec 03 2004


STATUS

approved



