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

Author

Zak Seidov, Apr 03 2011

Keywords

• nonn

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

Crossrefs

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

Programs

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

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

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