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Integers k such that k*28*c + 1 is prime for c = 1, 2, 4, 7 and 14.
3

%I #16 Sep 19 2019 19:49:13

%S 2136,2211,4071,5106,5430,9000,10656,17655,18315,20220,20805,21381,

%T 22356,22920,23025,29616,37050,39261,45795,49920,55686,60435,62205,

%U 64380,79356,81345,91455,94800,95910,96285,105336,108585,111885,118626

%N Integers k such that k*28*c + 1 is prime for c = 1, 2, 4, 7 and 14.

%C The product of the 5 primes is a Carmichael number. 28=1+2+4+7+14.

%D H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th ed., 1999, exercise 8.4.

%H Amiram Eldar, <a href="/A067199/b067199.txt">Table of n, a(n) for n = 1..10000</a>

%e 2136 results in Carmichael number 599966117492747584686619009.

%t aQ[n_] := AllTrue[{1, 2, 4, 7, 14}, PrimeQ[28 * n * # + 1] &]; Select[Range[10^5], aQ] (* _Amiram Eldar_, Sep 19 2019 *)

%Y Cf. A002997, A046025 (based on 6 instead of 28, exercise 8.3 in Davenport), A112428.

%K nonn,easy

%O 1,1

%A _Frank Ellermann_, Feb 19 2002

%E Offset corrected by _Amiram Eldar_, Sep 19 2019