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A133521 Smallest k such that p(n)^5 - k is prime where p(n) is the n-th prime. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A332991 A132530 A316389 * A122158 A178223 A033180

Adjacent sequences:  A133518 A133519 A133520 * A133522 A133523 A133524

KEYWORD

easy,nonn,changed

AUTHOR

Carl R. White, Sep 14 2007

STATUS

approved

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Last modified September 30 17:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)