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A122735 Smallest prime of the form (n^k - k^n) for k>1, or 1 if such prime does not exist. 4
1, 7, 17, 1, 6102977801, 162287, 79792265017612001, 8375575711, 2486784401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(10) = 10^273 - 273^10 is too large to include.

a(16) = 1 because primes of the form (16^k - k^16) do not exist, since 16^k - k^16 = (4^k - k^4)(4^k + k^4).

The corresponding numbers k such that a(n) = (n^k - k^n) are listed in A128355(n) = {0,5,4,0,14,7,20,11,10,273,14,13,38,89,68,0,...}, where k = 0 corresponds for definite a(n) = 1. Currently a(n) is not known for n = {17,18,22,25,26,27,28,...}.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

a(1) = 1 because (1^k - k^1) = (1 - k) < 0 for k > 1.

a(2) = 7 because 2^5 - 5^2 = 7 is prime, but (2^k - k^2) is not prime for 1 < k < 5, (2^2 - 2^2) = 0, (2^3 - 3^2) = -1, (2^4 - 4^2) = 0.

a(4) = 1 because prime of the form (4^k - k^4) does not exist, 4^k - k^4 = (2^k - k^2)(2^k + k^2).

a(12) = 83695120256591 = 12^13 - 13^12 = A024152[ A122003(2) ].

CROSSREFS

Cf. A024152, A122003.

Cf. A128355.

Sequence in context: A101122 A090535 A107778 * A094464 A224795 A138449

Adjacent sequences:  A122732 A122733 A122734 * A122736 A122737 A122738

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Sep 24 2006, corrected Mar 03 2007

STATUS

approved

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Last modified May 25 22:17 EDT 2019. Contains 323576 sequences. (Running on oeis4.)