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A110905 a(n) is the least number k such that k*prime(n)# - 1 is prime and (k*prime(n)# - 1)^2 - 2 is a Chen prime. 0
2, 1, 1, 11, 1, 6, 41, 17, 8, 13, 14, 107, 84, 23, 4, 101, 13, 89, 211, 58, 83, 75, 260, 414, 35, 39, 871, 79, 27, 42, 915, 44, 349, 142, 249, 404, 140, 84, 1068, 693, 972, 236, 1571, 1200, 298, 423, 970, 183, 173, 659, 523, 645, 1596, 448, 40, 201, 195, 1859, 427, 1732 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

2*2-1 = 3, (2*2-1)^2-2 = 7, 3 and 7 are primes, so a(1) = 2.

11*2*3*5*7-1 = 2309, (11*2*3*5*7-1)^2-2 = 5331479, 2309 and 5331479 are primes, so a(4) = 11.

MATHEMATICA

chenQ[n_] := PrimeQ[n] && PrimeOmega[n+2] <= 2; a[n_] := Module[{p = Product[Prime[i], {i, 1, n}], k = 0}, While[!PrimeQ[k*p - 1] || !chenQ[(k*p-1)^2-2], k++]; k]; Array[a, 60] (* Amiram Eldar, Sep 11 2021 *)

PROG

(PARI) isok(k, q) = if (isprime(k*q-1), my(c=(k*q-1)^2-2); (isprime(c) && (bigomega(c+2)<=2)));

a(n) = my(k=1, q=prod(i=1, n, prime(i))); while (!isok(k, q), k++); k; \\ Michel Marcus, Sep 11 2021

CROSSREFS

Cf. A002110, A109611.

Sequence in context: A064307 A165883 A260950 * A205447 A297544 A297802

Adjacent sequences:  A110902 A110903 A110904 * A110906 A110907 A110908

KEYWORD

nonn

AUTHOR

Pierre CAMI, Sep 21 2005

STATUS

approved

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Last modified December 3 15:34 EST 2021. Contains 349463 sequences. (Running on oeis4.)