A346419 a(n) is twice the coefficient of 1 in the fundamental unit of Q(sqrt(A000037(n))) where A000037 lists the nonsquare numbers (Version 2).

2, 4, 1, 10, 16, 2, 6, 20, 4, 3, 30, 8, 8, 2, 340, 1, 5, 394, 48, 10, 10, 4, 16, 5, 22, 3040, 2, 46, 70, 12, 12, 74, 50, 6, 64, 26, 6964, 20, 1, 48670, 96, 4, 2, 100, 3, 7, 10, 178, 30, 302, 198, 1060, 8, 39, 126, 16, 16, 130, 97684, 8, 25, 502, 6960, 2, 2136, 86, 4, 340, 9, 106, 160, 1, 18, 164, 5, 9, 20810

Offset

1,1

Links

Table of n, a(n) for n=1..77.

S. R. Finch, Class number theory

Steven R. Finch, Class number theory [Cached copy, with permission of the author]

Eric Weisstein's World of Mathematics, Fundamental Unit.

Mathematica

nonSquares = Select[Range[72], !IntegerQ[Sqrt[#]]& ]; 2*NumberFieldFundamentalUnits[Sqrt[#]][[1, 2, 1]] & /@ nonSquares (* Jean-François Alcover, Nov 09 2012 *)

Prog

(PARI) for(n=1, 30, if(!issquare(n), print1(abs(2*polcoeff(lift(bnfinit(x^2-n).fu[1]), 0)), ", "))) /* Ralf Stephan, Sep 18 2013; updated by Michel Marcus, Jun 25 2020 */

Crossrefs

Cf. A000037, A346420, A048941, A048942.

Sequence in context: A135330 A135328 A355144 * A048941 A308300 A246188

Adjacent sequences: A346416 A346417 A346418 * A346420 A346421 A346422

Keyword

nonn

Author

Sean A. Irvine

Status

approved