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A121877

Numbers k such that (5^k - 3^k)/2 = A005059(k) is prime.

13, 19, 23, 31, 47, 127, 223, 281, 2083, 5281, 7411, 7433, 19051, 27239, 35863, 70327, 128941, 147571, 182099, 866029 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`All terms are primes. Their indices are listed in A123704.` `Corresponding primes are listed in A123705.` `If it exists, a(17) > 125000. - Robert Price, Aug 15 2011` `If it exists, a(21) > 1000000. - Jon Grantham, Jul 29 2023`
	LINKS	`Table of n, a(n) for n=1..20.` `OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b).` `Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.`
	FORMULA	`a(n) = prime(A123704(n)).`
	MATHEMATICA	`Do[f=(5^n-3^n)/2; If[PrimeQ[f], Print[{n, f}]], {n, 1, 300}]`
	PROG	`(PARI) forprime(p=2, 1e4, if(ispseudoprime((5^p-3^p)>>1), print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011`
	CROSSREFS	`Cf. A005058, A005059, A109347, A120612, A081186, A121824, A123704, A123705.` `Sequence in context: A007627 A180525 A257590 * A109902 A214031 A250293` `Adjacent sequences: A121874 A121875 A121876 * A121878 A121879 A121880`
	KEYWORD	`nonn,hard,more`
	AUTHOR	`Alexander Adamchuk, Aug 31 2006, Oct 08 2006`
	EXTENSIONS	`More terms from Farideh Firoozbakht, Oct 11 2006` `a(13)-a(16) from Robert Price, Aug 15 2011` `a(17)-a(19) from Kellen Shenton, May 18 2022` `a(20) from Jon Grantham, Jul 29 2023`
	STATUS	`approved`

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Last modified August 1 08:32 EDT 2024. Contains 374811 sequences. (Running on oeis4.)