A133521 Smallest k such that p(n)^5 - k is prime where p(n) is the n-th prime.

1, 2, 4, 20, 4, 2, 18, 18, 16, 6, 2, 6, 24, 12, 36, 22, 10, 8, 8, 24, 20, 86, 22, 6, 18, 42, 26, 6, 50, 52, 20, 12, 48, 2, 196, 68, 18, 14, 16, 16, 18, 2, 10, 6, 16, 38, 2, 36, 6, 2, 16, 42, 18, 42, 40, 34, 22, 2, 38, 4, 36, 52, 26, 132, 36, 28, 24, 74, 46, 36, 4, 16, 8, 24, 80, 16

Offset: 1

Author

Carl R. White, Sep 14 2007

Keywords

• easy
• nonn

Examples

			p(10)=29, 29^5 = 20511149; for odd k and n > 1, p(n)^r - k is even and thus not prime, so we only need consider even k.
for k = 2: 20511149 - 2 = 20511147, which is 3 * 23 * 297263 and not prime.
for k = 4: 20511149 - 4 = 20511145, which is 5 * 4102229, also not prime.
for k = 6: 20511149 - 6 = 20511141, which is prime, so 6 is the smallest number that can be subtracted from 20511149 to make another prime.
Hence a(10) = 6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A050997, A054271, A091666, A133517, A133518, A133519, A133520, A133522, (A001223).

Programs

Mathematica

#-NextPrime[#,-1]&/@(Prime[Range[80]]^5) (* Harvey P. Dale, Sep 27 2020 *)