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.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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: A116497 A346685 A133543 * A321670 A356071 A254497

Adjacent sequences: A294028 A294029 A294030 * A294032 A294033 A294034

Keyword

nonn

Author

Amiram Eldar, Oct 22 2017

Status

approved