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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The number (7m+1)(8m+1)(11m+1) is a 3-factor 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 1000-digit 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

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Last modified January 27 11:39 EST 2023. Contains 359839 sequences. (Running on oeis4.)