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A188547 Numbers n such that m=(n^2+1)/2, p=(m^2+1)/2, q=(p^2+1)/2, and r=(q^2+1)/2 are all prime. 6
4949, 6051, 169219, 183241, 560769, 1113621, 1306689, 1370269, 1421869, 1485561, 1640711, 1730709, 1876351, 1967769, 2147661, 2217351, 2293939, 2428461, 2440871, 3346661, 3625139, 3625889, 3763969, 3991209, 4020711, 4728141, 5219691, 5547221, 5554939, 5965699, 7345719, 8495879 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(1) = 4949 = A188546(6) = A116945(53).

Subsequence of A188546.

Numbers n which generate 4 primes under the first four iterations of the map n-> A002731(n).

Among first 10000 terms, there are 1072 primes, the first a(3) = 169219 and the last a(10000) = 16541600731. - Zak Seidov, Jan 16 2019

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000, replacing an earlier file from Zak Seidov

MATHEMATICA

s={}; Do[If[PrimeQ[m=(n^2+1)/2] && PrimeQ[p=(m^2+1)/2] && PrimeQ[q=(p^2+1)/2] && PrimeQ[r=(q^2+1)/2], AppendTo[s, n]], {n, 1, 10000000, 2}]; s

PROG

(PARI) v=vector(10^4); i=0; forstep(n=1, 9e99, 2, if(isprime(m=(n^2+1)/2) && isprime(p=(m^2+1)/2) && isprime(q=(p^2+1)/2) && isprime(r=(q^2+1)/2), v[i++]=n; if(i==#v, return))) \\ Charles R Greathouse IV, Apr 12 2011

(MAGMA) r:=func< k | (k^2+1) div 2 >; [ n: n in [1..1000000 by 2] | IsPrime(r(n)) and IsPrime(r(r(n))) and IsPrime(r(r(r(n))))and IsPrime(r(r(r(r(n)))))]; // Vincenzo Librandi, Jan 16 2019

CROSSREFS

Cf. A002731, A105318, A116945, A188546, A187431.

Sequence in context: A241934 A185850 A260939 * A037044 A251847 A225718

Adjacent sequences:  A188544 A188545 A188546 * A188548 A188549 A188550

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 03 2011

STATUS

approved

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Last modified August 18 22:03 EDT 2019. Contains 326109 sequences. (Running on oeis4.)