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Least k such that n^n + k + 1 is a prime.
1

%I #10 Aug 20 2019 09:24:56

%S 0,0,1,0,11,6,3,42,9,18,61,34,15,26,27,12,73,106,17,90,31,86,13,94,95,

%T 42,67,134,119,18,57,6,57,62,53,30,41,114,9,156,109,12,3,402,121,456,

%U 533,36,17,30,225,252,19,192,101,176,391,44,193,256,101,78,453

%N Least k such that n^n + k + 1 is a prime.

%H Amiram Eldar, <a href="/A193813/b193813.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = A098682(n) - n^n -1. - _Michel Marcus_, Aug 20 2019

%e a(5) = 11 because 5^5 + 11 + 1 = 37 is prime.

%t a={};Do[k = 0; While[ !PrimeQ[n^n + k + 1], k++ ]; AppendTo[a, k], {n, 1, 100} ];a

%o (PARI) a(n) = nextprime(n^n) - n^n - 1; \\ _Michel Marcus_, Aug 20 2019

%Y Cf. A000312, A098682.

%K nonn

%O 1,5

%A _Michel Lagneau_, Aug 06 2011