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.

Original entry on oeis.org

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, 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, 98, 15, 4, 27, 24, 2, 4, 17343, 34, 19, 24, 15, 56, 6, 90, 5, 2, 85
Offset: 1

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Author

Kevin P. Thompson, Jun 12 2023

Keywords

Comments

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.

Examples

			For n = 3:
k = 1: 1^3 - 3 = -2 < 0 so ignore.
k = 2: 2^3 - 3 = 5 which is not semiprime.
k = 3: 3^3 - 3 = 24 = 2 * 2 * 2 * 3 which is not semiprime.
k = 4: 4^3 - 3 = 61 which is not semiprime.
k = 5: 5^3 - 3 = 122 = 2 * 61 which is semiprime.
Therefore, a(3) = 5 since k = 5 is the first value for which k^3 - 3 is semiprime.
		

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