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A133519 Smallest k such that p(n)^4 - k is prime where p(n) is the n-th prime. 7
3, 2, 6, 2, 2, 2, 24, 14, 18, 2, 8, 8, 2, 2, 12, 2, 2, 24, 24, 38, 2, 8, 2, 54, 12, 2, 12, 12, 44, 18, 14, 18, 12, 32, 12, 24, 38, 14, 12, 12, 54, 2, 50, 8, 32, 8, 12, 14, 24, 8, 8, 2, 2, 12, 18, 30, 50, 12, 2, 24, 12, 2, 32, 2, 84, 12, 8, 12, 8, 74, 14, 18, 2, 20, 24, 14, 2, 14, 14, 2, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

p(3)=5, 5^4 = 625; 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: 625 - 2 = 623, which is 7 * 89 and not prime.

for k = 4: 625 - 4 = 621, which is 3^3 * 23, also not prime.

for k = 6: 625 - 6 = 619, which is prime, so 6 is the smallest number that can be subtracted from 625 to make another prime.

Hence a(3) = 6.

CROSSREFS

Cf. A030814, A054271, A091666, A133517, A133518, A133520, A133521, A133522, (A001223).

Sequence in context: A019761 A188614 A290798 * A135223 A143310 A131897

Adjacent sequences:  A133516 A133517 A133518 * A133520 A133521 A133522

KEYWORD

easy,nonn

AUTHOR

Carl R. White, Sep 14 2007

STATUS

approved

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Last modified September 18 10:31 EDT 2020. Contains 337166 sequences. (Running on oeis4.)