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

Author

Amiram Eldar, Oct 22 2017

Keywords

• nonn

Examples

			20543425 generates 11236306070625187487140801 + 8309959597401596721108558352203300 k which are Carmichael numbers for k = 0 to 4.
		

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.

Crossrefs

Cf. A002997.

Subsequence of A017533.

Programs

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]