A382066 - OEIS

A382066

a(n) = Sum_{k=1..prime(n)-1} (-k/prime(n)) * 3^(k-1) / 2, where (p/q) is the Legendre symbol of p and q.

%I #19 Mar 31 2025 21:19:51

%S 1,8,151,8083,70568,8910416,39392803,7701058213,2325990648824,

%T 43563061207573,19999898090377928,2566793589644124992,

%U 10627327735475477203,2179055220073884519235,630486036620986837882904,646895254841829205782412249,5802709167332592724735012664

%N a(n) = Sum_{k=1..prime(n)-1} (-k/prime(n)) * 3^(k-1) / 2, where (p/q) is the Legendre symbol of p and q.

%C All terms are integers since Sum_{k=1..p-1} (-k/p) * 3^(k-1) is even for any odd prime p.

%H Steven Lu, <a href="/A382066/b382066.txt">Table of n, a(n) for n = 2..316</a>

%t Table[Sum[KroneckerSymbol[-i, q] 3^(i - 1), {i, q - 1}], {q, Prime /@ Range[2, 18]}]/2

%K nonn

%O 2,2

%A _Steven Lu_, Mar 14 2025