NAME
Only k >= 0 such that, for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^(2^k ) + 1.
EXAMPLE
A093179(5) = 641, A007117(5) = 5 and the only k >= 0 such that, for every odd r > 0, 641 divides the generalized Fermat number (5^r)^(2^k ) + 1 is 5; so a(5) = 5.
Discussion
Sat Jul 15
06:01
N. J. A. Sloane: added missing parens
NAME
Least Only k >= 0 such that , for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^2^k + 1.
COMMENTS
a(n) is the only k >= 0 such that, for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^2^k + 1 (see Theorem 2.3 and Theorem 2.5 of my article in the links).
EXAMPLE
A093179(5) = 641, A007117(5) = 5 and the least positive integer only k >= 0 such that , for every odd r > 0, 641 divides the generalized Fermat number (5^r)^2^k + 1 is 5, ; so a(5) = 5.
NAME
Least positive integer k >= 0 such that A093179(n) divides the generalized Fermat number A007117(n)^2^k + 1.
COMMENTS
If f > 17 a(n) is a term of A307843 and r the only k > = 0 is such that, for every odd, then f r > 0, A093179(n) divides the generalized Fermat number (((f - 1)/2^A007117(n + 2))^r)^2^a(n) k + 1 (cf. see Theorem 2.3 and Theorem 2.5 of my article in the links), which equals A007117(n)^2^k + 1 by taking f = A093179(n) and r = 1.
Discussion
Tue Jun 13
15:13
Lorenzo Sauras Altuzarra: Corrected and simplified.
COMMENTS
If f > 17 is a term of A307843 and r > 0 is odd, then f divides the generalized Fermat number (((f - 1)/2^(n + 2))^r)^2^a(n) + 1 (cf. Theorem 2.3 of my article in the links); , which equals A007117(n)^2^k + 1 by taking f = A093179(n) and r = 1.