cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A361803 Least k > 1 such that k^n - n > 1 is semiprime, or 0 if no such k exists.

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%I A361803 #22 Jun 25 2023 18:20:51
%S A361803 5,4,5,3,6,2,2,5,8,3,4,11,15,5,2,0,4,2,14,7,48,42,6,35,2,7,602,3,16,
%T A361803 13,2,3,2,6,37,3185,6,9,2,33,28,2,20,9,2,135,6,5,2,49,100,5,166,5,4,9,
%U A361803 98,15,4,27,24,2,4,17343,34,19,24,15,56,6,90,5,2,85
%N A361803 Least k > 1 such that k^n - n > 1 is semiprime, or 0 if no such k exists.
%C A361803 For n = 16, k^16 - 16 = (k^8 - 4)(k^8 + 4) = (k^4 - 2)(k^4 + 2)(k^8 + 4) always has at least three factors, so a(16) = 0. Similarly for any n of the form (2m)^4, so a(A016744(n)) = 0.
%H A361803 Kevin P. Thompson, <a href="/A361803/b361803.txt">Table of n, a(n) for n = 1..115</a>
%H A361803 Kevin P. Thompson, <a href="/A361803/a361803.txt">Table of n, a(n) for n = 1..154 with uncertain values</a>
%e A361803 For n = 3:
%e A361803 k = 1: 1^3 - 3 = -2 < 0 so ignore.
%e A361803 k = 2: 2^3 - 3 = 5 which is not semiprime.
%e A361803 k = 3: 3^3 - 3 = 24 = 2 * 2 * 2 * 3 which is not semiprime.
%e A361803 k = 4: 4^3 - 3 = 61 which is not semiprime.
%e A361803 k = 5: 5^3 - 3 = 122 = 2 * 61 which is semiprime.
%e A361803 Therefore, a(3) = 5 since k = 5 is the first value for which k^3 - 3 is semiprime.
%Y A361803 Cf. A001358, A016744, A130827.
%K A361803 nonn
%O A361803 1,1
%A A361803 _Kevin P. Thompson_, Jun 12 2023