A197631 Lerch remainders: the Lerch quotient A197630 of the n-th prime p modulo p, where n > 1.

0, 3, 5, 5, 6, 12, 13, 3, 7, 19, 2, 21, 34, 33, 52, 31, 51, 38, 32, 25, 25, 25, 53, 22, 98, 0, 79, 42, 63, 123, 75, 11, 11, 39, 34, 151, 36, 137, 22, 49, 19, 144, 41, 44, 21, 5, 122, 4, 111, 10, 228, 194, 148, 20, 217, 193, 157, 202, 152, 87, 93, 30, 219

Offset: 2

Author

Jonathan Sondow, Oct 16 2011

Keywords

• nonn
• easy

Examples

			a(3) = A197630(3) mod Prime(3) = 13 mod 5 = 3.
		

Links

• J. B. Dobson A note on Lerch primes, arXiv:1311.2242 [math.NT], 2014.
• J. B. Dobson A Characterization of Wilson-Lerch Primes, Integers, 16 (2016), A51.
• Jonathan Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113 [math.NT], 2011-2012.
• Jonathan Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.

Crossrefs

Cf. A197630, A197632.

Programs

PARI

a(n) = my(p=prime(n), m=p-1); sum(k=1, m, k^m, -p-m!)/p^2 % p;
vector(100, n, a(n+1)) \\ Altug Alkan, Nov 22 2015

Formula

a(n) = A197630(n) mod Prime(n), with n >= 2.