A110905 - OEIS

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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.

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: A370950 A260950 A372960 * A205447 A297544 A297802

Adjacent sequences: A110902 A110903 A110904 * A110906 A110907 A110908

KEYWORD

nonn

AUTHOR

Pierre CAMI, Sep 21 2005

STATUS

approved