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A323427 Primes p such that the concatenation of p^2, p and 1 is prime. 2
2, 5, 17, 41, 89, 173, 191, 197, 293, 311, 353, 479, 491, 647, 797, 857, 887, 911, 971, 1097, 1181, 1319, 1523, 1847, 2003, 2069, 2153, 2351, 2411, 2459, 2549, 2693, 2699, 2729, 2837, 2843, 2957, 2963, 3011, 3041, 3089, 3359, 3407, 3533, 3557, 3581, 3761, 3767, 3797, 4133, 4289, 4547, 4787, 4937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms == 2 (mod 3).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3)=17 is a term because 17 and 289171 are primes, where 17^2=289.

MAPLE

cat3:= proc(x) local t;

  t:= 10*x+1;

  x^2*10^(1+ilog10(t))+t

end proc:

select(t -> isprime(t) and isprime(cat3(t)), [2, seq(i, i=5..10000, 6)]);

MATHEMATICA

ppQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n^2, n, 1]]]; Select[Prime[Range[500]], ppQ] (* Vincenzo Librandi, Jan 15 2019 *)

CROSSREFS

Cf. A323428.

Sequence in context: A122566 A263638 A118500 * A080898 A081763 A013918

Adjacent sequences:  A323424 A323425 A323426 * A323428 A323429 A323430

KEYWORD

nonn,base

AUTHOR

J. M. Bergot and Robert Israel, Jan 14 2019

STATUS

approved

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Last modified October 17 19:44 EDT 2019. Contains 328128 sequences. (Running on oeis4.)