login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..23.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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