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 A294031 Numbers n such that n == 1 (mod 12) and n+1, 12n+1, 18n+1, 36n+1, 72n+1, 108n+1 and 144n+1 are all primes, so N = (6n+1)(12n+1)(18n+1), (36n+1)N, (72n+1)N, (108n+1)N and (144n+1)N are 5 Carmichael numbers in an arithmetic progression. 0
 20543425, 80993605, 112608685, 255063865, 307510105, 367621765, 382017685, 400463665, 409631425, 430786405, 536835565, 675787105, 950572525, 1040986765, 1139137825, 1214553025, 1404069205, 1456119805, 1560636805, 1608308905, 1796972905, 1805035225, 1823195605 (list; graph; refs; listen; history; text; internal format)
 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. Sequence in context: A251458 A116497 A133543 * A321670 A254497 A254490 Adjacent sequences:  A294028 A294029 A294030 * A294032 A294033 A294034 KEYWORD nonn AUTHOR Amiram Eldar, Oct 22 2017 STATUS approved

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Last modified August 13 00:27 EDT 2020. Contains 336441 sequences. (Running on oeis4.)