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

%I

%S 17,101,28901,324901,608401,902501,2016401,5664401,7452901,14822501,

%T 16974401,18490001,34222501,40449601,41731601,46240001,48580901,

%U 50410001,52417601,76038401,92736901,103022501,111936401,121220101,124768901,139948901,151290001

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

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

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

%H Donovan Johnson and Charles R Greathouse IV, <a href="/A234693/b234693.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Johnson)

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

%p 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:

%o (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

%Y Cf. A002496, A144255, A085722.

%K nonn

%O 1,1

%A _Michel Lagneau_, Dec 29 2013

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)