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A260903 Numbers n such that (2^(2n+7) * 5^(2n+5) + 740711) / 33 is prime (n > 0). 5
11, 26, 31, 205, 307, 6875, 33161 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 11:22 EDT 2021. Contains 346289 sequences. (Running on oeis4.)