A245016 Smallest number k such that P=k*prime(n+1)*(prime(n)-1)+1, Q=k*prime(n+1)*P+1, R=(prime(n)-1)*Q+1 and P, Q, and R are all prime numbers.

10, 1986, 6, 696, 200, 222, 6510, 1050, 630, 756, 56, 726, 798, 126, 114, 6600, 166, 62, 1422, 12034, 170, 34944, 1410, 912, 2880, 2558, 1200, 9350, 5148, 1506, 5040, 384, 2250, 1680, 114, 396, 3248, 2310, 18930, 30810, 938, 1176, 1020, 2022, 8500, 142, 1760, 1218

Offset

2,1

Comments

Q= x^2 + x + p(n) with x = k*p(n+1)*(p(n)-1), a polynomial prime.

Links

Pierre CAMI, Table of n, a(n) for n = 2..10001

Mathematica

snk[n_]:=Module[{pr=Prime[n], pr1=Prime[n+1], k=1, p, q, r}, p=k*pr1*(pr-1)+1; q=k*pr1*p+1; r=(pr-1)*q+1; While[!AllTrue[{p, q, r}, PrimeQ], k++; p=k*pr1*(pr-1)+1; q=k*pr1*p+1; r=(pr-1)*q+1; ]; k]; Array[snk, 50, 2] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 09 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i
DIM j
DIM k
DIM n, 1
OPENFILEOUT myf, a(n)
LABEL loop1
SET n, n+1
SET k, 0
SET i, p(n)-1
SET j, p(n+1)
LABEL loop2
SET k, k+2
PRP k*i*j+1
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
PRP k*j*(k*i*j+1)+1
IF ISPRP THEN GOTO b
GOTO loop2
LABEL b
PRP i*(k*j*(k*i*j+1)+1)+1
IF ISPRP THEN GOTO c
GOTO loop2
LABEL c
WRITE myf, k
GOTO loop1

Crossrefs

Cf A005846.

Sequence in context: A024138 A261603 A346543 * A294174 A177359 A228294

Adjacent sequences: A245013 A245014 A245015 * A245017 A245018 A245019

Keyword

nonn

Author

Pierre CAMI, Sep 17 2014

Status

approved