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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 25 12:47 EDT 2020. Contains 337344 sequences. (Running on oeis4.)