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A142959

Numbers k such that both (k!)^2 + k! + 1 and (k!)^2 + 1 are prime.

1, 2, 3, 4, 76

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OFFSET

1,2

COMMENTS

For the numbers of digits of the associated primes, see A142960.

a(6) > 150000, because A046029(15) > 150000 and A046029(14) = 127162 is not a term here since (127162!)^2 + 127162! + 1 is divisible by 2049703. - Giovanni Resta, Aug 12 2025

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 76, pp 26, Ellipses, Paris 2008.

LINKS

Table of n, a(n) for n=1..5.

FORMULA

A046029 INTERSECT A051856. - R. J. Mathar, Aug 08 2008

MATHEMATICA

Select[Range[80], With[{c=#!}, AllTrue[c^2+{c+1, 1}, PrimeQ]]&] (* Harvey P. Dale, Aug 11 2025 *)

CROSSREFS

Cf. A142960, A046029, A051856.

Sequence in context: A066776 A115901 A073325 * A173573 A037395 A009496

Adjacent sequences: A142956 A142957 A142958 * A142960 A142961 A142962

KEYWORD

nonn,hard,more

AUTHOR

Lekraj Beedassy, Jul 13 2008

STATUS

approved

URL: https://oeis.org/A142959

⇱ A142959 - OEIS