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A361803
Least k > 1 such that k^n - n > 1 is semiprime, or 0 if no such k exists.
2
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
1,1
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.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin P. Thompson, Jun 12 2023
STATUS
approved