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

%I A197631 #36 Nov 08 2024 07:59:34
%S A197631 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,
%T A197631 79,42,63,123,75,11,11,39,34,151,36,137,22,49,19,144,41,44,21,5,122,4,
%U A197631 111,10,228,194,148,20,217,193,157,202,152,87,93,30,219
%N A197631 Lerch remainders: the Lerch quotient A197630 of the n-th prime p modulo p, where n > 1.
%H A197631 J. B. Dobson <a href="http://arxiv.org/abs/1311.2242">A note on Lerch primes</a>, arXiv:1311.2242 [math.NT], 2014.
%H A197631 J. B. Dobson <a href="http://www.integers-ejcnt.org/vol16.html">A Characterization of Wilson-Lerch Primes</a>, Integers, 16 (2016), A51.
%H A197631 Jonathan Sondow, <a href="http://arxiv.org/abs/1110.3113">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, in Proceedings of CANT 2011, arXiv:1110.3113 [math.NT], 2011-2012.
%H A197631 Jonathan Sondow, <a href="http://dx.doi.org/10.1007/978-1-4939-1601-6_17">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.
%F A197631 a(n) = A197630(n) mod Prime(n), with n >= 2.
%e A197631 a(3) = A197630(3) mod Prime(3) = 13 mod 5 = 3.
%o A197631 (PARI) a(n) = my(p=prime(n), m=p-1); sum(k=1, m, k^m, -p-m!)/p^2 % p;
%o A197631 vector(100, n, a(n+1)) \\ _Altug Alkan_, Nov 22 2015
%Y A197631 Cf. A197630, A197632.
%K A197631 nonn,easy
%O A197631 2,2
%A A197631 _Jonathan Sondow_, Oct 16 2011