A260903 Numbers n such that (2^(2n+7) * 5^(2n+5) + 740711) / 33 is prime (n > 0).

11, 26, 31, 205, 307, 6875, 33161

Offset

1,1

Comments

The numbers that follow the expression in the definition have this form: (12) concatenated n times and prepended to 34567.

Empirical observations: primes alternate with nonprimes. 6th (nonprime) and 7th (prime) terms correspond to probable primes. Up to which term the pattern will hold?

(2^(2*a(n)+7) * 5^(2*a(n)+5) + 740711) has 7 proper divisors.

Links

Table of n, a(n) for n=1..7.

Example

11 appears because 121212121212121212121234567 ('12' concatenated 11 times and prepended to '34567') is prime.

Maple

A260903:=n->`if`(isprime((2^(2*n+7) * 5^(2*n+5) + 740711)/33), n, NULL): seq(A260903(n), n=1..500); # Wesley Ivan Hurt, Nov 27 2015

Mathematica

Select[Range[500], PrimeQ[(2^(2# + 7) * 5^(2# + 5) + 740711)/33] &] (* or *)
Select[Range[50], DivisorSigma[0, (2^(2# + 7) * 5^(2# + 5) + 740711)] - 1 == 7 &] (* inefficient *)

Prog

(Magma) [n: n in [1..250] | IsPrime((2^(2*n+7) * 5^(2*n+5) + 740711) div 33)]; // Vincenzo Librandi, Nov 18 2015
(PARI) is(n)=isprime((2^(2*n+7)*5^(2*n+5) + 740711)/33) \\ Anders Hellström, Nov 18 2015

Crossrefs

Sequence in context: A066956 A250611 A137015 * A316315 A251268 A174223

Adjacent sequences: A260900 A260901 A260902 * A260904 A260905 A260906

Keyword

nonn,base,hard,more

Author

Mikk Heidemaa, Nov 17 2015

Status

approved