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A339639 a(n) is the sum of the Wieferich and Wall-Sun-Sun residues of prime(n). 0
3, 6, 20, 35, 110, 78, 493, 114, 736, 783, 961, 518, 2542, 2752, 2820, 3392, 1062, 5124, 1139, 4047, 8322, 5372, 5727, 979, 9118, 19089, 8343, 3959, 10137, 16159, 3937, 10611, 15207, 20433, 32184, 17516, 19782, 37001, 15197, 23009, 40096, 50499, 27504, 26055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If a(n) = 0 then prime(n) is both a Wieferich prime (A001220) and a Wall-Sun-Sun (Fibonacci-Wieferich) prime.

If the first case of Fermat's last theorem fails for a prime p, that prime is both a Wieferich prime (cf. Wieferich, 1909) and a Wall-Sun-Sun prime (cf. Sun, 1992).

LINKS

Table of n, a(n) for n=1..44.

Zhi-Wei Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithemtica, Vol. 60, No. 4 (1992), 371-388.

A. Wieferich, Zum letzten Fermat'schen Theorem, Journal für die reine und angewandte Mathematik, 136 (1909), 293-302, DOI:10.1515/crll.1909.136.293.

FORMULA

a(n) = A196202(n) + A113650(n) - 1.

PROG

(PARI) a(n) = my(p=prime(n)); lift(Mod([1, 1; 1, 0]^(p-kronecker(p, 5)), p^2)[1, 2]) + lift(Mod(2, p^2)^(p-1)) - 1

CROSSREFS

Cf. A001220, A113650, A196202.

Sequence in context: A290784 A176993 A276748 * A081181 A062164 A265112

Adjacent sequences:  A339636 A339637 A339638 * A339640 A339641 A339642

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Dec 11 2020

STATUS

approved

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Last modified January 17 23:59 EST 2021. Contains 340249 sequences. (Running on oeis4.)