A224496 Smallest k such that k*2*p(n)^2+1=q is prime, k*2*q^2+1=r, k*2*r^2+1=s, k*2*r^2+1=t, r, s, and t are also prime.

386, 2769, 96656, 5366, 420, 34454, 65039, 192215, 458367, 24735, 27155, 777, 736254, 80297, 279927, 113429, 650474, 238919, 8229, 1284345, 642789, 333141, 11510, 1009271, 932, 395126, 1202174, 25811, 204534, 16286, 22094, 2661131, 22530, 128225, 56225, 900

Offset

1,1

Comments

Conjecture: a(n) exist for all n

t=k*2*(k*2*(k*2*(k*2*p(n)^2+1)^2+1)^2+1)^2+1

s=k*2*(k*2*(k*2*p(n)^2+1)^2+1)^2+1

r=k*2*(k*2*p(n)^2+1)^2+1

q=k*2*p(n)^2+1

Links

Pierre CAMI, Table of n, a(n) for n = 1..80

Mathematica

a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[q = k*2*p^2 + 1] && PrimeQ[r = k*2*q^2 + 1] && PrimeQ[s = k*2*r^2 + 1] && PrimeQ[k*2*s^2 + 1], Return[k]]]; Table[ Print[an = a[n]]; an , {n, 1, 36}] (* Jean-François Alcover, Apr 12 2013 *)

Prog

(PFGW and SCRIPTIFY)
SCRIPT
DIM k
DIM i, 0
DIM q
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL a
SET i, i+1
IF i>34 THEN END
SET k, 0
LABEL b
SET k, k+1
SETS t, %d, %d, %d\,; k; i; p(i)
SET q, k*2*p(i)^2+1
PRP q, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
SET q, k*2*q^2+1
PRP q, t
IF ISPRP THEN GOTO d
GOTO b
LABEL d
SET q, k*2*q^2+1
PRP q, t
IF ISPRP THEN GOTO e
GOTO b
LABEL e
SET q, k*2*q^2+1
PRP q, t
IF ISPRP THEN WRITE myf, t
IF ISPRP THEN GOTO a
GOTO b

Crossrefs

Cf. A224489, A224490, A224491, A224492, A224193, A224494, A224495.

Sequence in context: A116316 A213115 A277988 * A230274 A230475 A116329

Adjacent sequences: A224493 A224494 A224495 * A224497 A224498 A224499

Keyword

nonn

Author

Pierre CAMI, Apr 08 2013

Status

approved