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A221902 Primes of the form 2*n^2 + 10*n + 3. 3

%I #15 Sep 08 2022 08:46:04

%S 31,103,211,751,1291,2371,2803,3271,5503,6151,8311,9103,9931,17851,

%T 23971,25303,32503,42331,49603,51511,68071,82003,94603,97231,105331,

%U 119551,122503,137803,157351,167611,171103,174631,192811,204151

%N Primes of the form 2*n^2 + 10*n + 3.

%C Conjecture: After the first term, 2^a(n)-1 is not prime; in other words, these primes (except 31) are included in A054723.

%C 2*a(n) + 19 is a square. - _Vincenzo Librandi_, Apr 10 2015

%H Vincenzo Librandi, <a href="/A221902/b221902.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Table[2 n^2 + 10 n + 3,{n, 500}],PrimeQ]

%o (Magma) [a: n in [1..500] | IsPrime(a) where a is 2*n^2 + 10*n + 3];

%Y Cf. Primes of the form 2*n^2+2*(2*k+3)*n+(2*k+1): A176549 (k=0), A154577 (k=2), A154592 (k=3), A154601 (k=4), A217494 (k=7), A217495 (k=10), A217496 (k=11), A217497 (k=12), A217498 (k=13), A217499 (k=16), A217500 (k=17), A217501 (k=18), A217620 (k=19), A217621 (k=21).

%Y Cf. A054723 (Prime exponents of nonprime Mersenne numbers).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 31 2013

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)