A234693 Primes of the form n^2 + 1 such that (n - 1)^2 + 1 and (n + 1)^2 + 1 are semiprimes.

17, 101, 28901, 324901, 608401, 902501, 2016401, 5664401, 7452901, 14822501, 16974401, 18490001, 34222501, 40449601, 41731601, 46240001, 48580901, 50410001, 52417601, 76038401, 92736901, 103022501, 111936401, 121220101, 124768901, 139948901, 151290001

Offset: 1

Author

Michel Lagneau, Dec 29 2013

Keywords

• nonn

Comments

The corresponding n are 4, 10, 170, 570, 780, 950, 1420, 2380...

Property: n^2 + 1 = p + q - 1 and for a(n) > 17, a(n) == 1 mod 100.

Examples

			101 = 10^2 + 1 is in the sequence because 9^2 + 1 = 2*41 and 11^2 + 1 = 2*61.
		

Links

• Donovan Johnson and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Johnson)

Crossrefs

Cf. A002496, A144255, A085722.

Programs

Maple

with(numtheory):for n from 1 to 10^5 do:n1:=n^2+1:n2:=(n+1)^2+1:n3:=(n+2)^2+1: if type(n2,prime)=true and bigomega(n1)=2 and bigomega(n3)=2 then printf(`%d, `,n2):else fi:od:

PARI

forstep(n=4,1e5,2,if(isprime(n^2+1) && isprime(n^2/2-n+1) && isprime(n^2/2+n+1), print1(n^2+1", "))) \\ Charles R Greathouse IV, Dec 29 2013