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A294031
Numbers k such that k == 1 (mod 12) and 6*k+1, 12*k+1, 18*k+1, 36*k+1, 72*k+1, 108*k+1 and 144*k+1 are all primes, so N = (6*k+1)*(12*k+1)*(18*k+1), (36*k+1)*N, (72*k+1)*N, (108*k+1)*N and (144*k+1)*N are 5 Carmichael numbers in an arithmetic progression.
1
20543425, 80993605, 112608685, 255063865, 307510105, 367621765, 382017685, 400463665, 409631425, 430786405, 536835565, 675787105, 950572525, 1040986765, 1139137825, 1214553025, 1404069205, 1456119805, 1560636805, 1608308905, 1796972905, 1805035225, 1823195605
OFFSET
1,1
REFERENCES
Andrzej Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad, Yugoslavia, 1972.
LINKS
Andrzej Rotkiewicz, Arithmetic progressions formed by pseudoprimes, Acta Mathematica et Informatica Universitatis Ostraviensis, Vol. 8, No. 1 (2000), pp. 61-74.
EXAMPLE
20543425 generates 11236306070625187487140801 + 8309959597401596721108558352203300 k which are Carmichael numbers for k = 0 to 4.
MATHEMATICA
aQ[n_]:=Mod[n, 12]==1 && AllTrue[{6n+1, 12n+1, 18n+1, 36n+1, 72n+1, 108n+1, 144n+1}, PrimeQ]; Select[Range[10^8], aQ]
CROSSREFS
Cf. A002997.
Subsequence of A017533.
Sequence in context: A346685 A133543 A373467 * A321670 A356071 A254497
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 22 2017
STATUS
approved