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

1,1

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.

Links

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

Example

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

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:

Prog

(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

Crossrefs

Cf. A002496, A144255, A085722.

Sequence in context: A215234 A145943 A331950 * A022677 A275919 A229425

Adjacent sequences: A234690 A234691 A234692 * A234694 A234695 A234696

Keyword

nonn

Author

Michel Lagneau, Dec 29 2013

Status

approved