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.

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

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