A290727 Analog of A085635, replacing "quadratic residue" (X^2) with "value of X^2+X".

1, 2, 6, 10, 14, 18, 30, 42, 66, 70, 90, 126, 198, 210, 330, 390, 450, 630, 990, 1170, 1386, 1638, 2142, 2310, 2730, 3150, 4950, 5850, 6930, 8190, 10710, 11970, 12870, 16830, 18018, 23562, 26334, 27846, 30030, 34650

Offset

1,2

Comments

Positions where R(k) = A290731(k)/k achieves a new minimum, i.e., R(k) < R(j), j = 0..k-1, R(0) = 2.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..116

Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. See Table 5.

Mathematica

a290731[n_] := Product[{p, e} = pe; If[p == 2, 2^(e-1), 1+Quotient[p^(e+1), (2p+2)]], {pe, FactorInteger[n]}];
Reap[For[r = 2; k = 1, k <= 35000, k++, t = a290731[k]/k; If[t<r, r = t; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Sep 03 2018, from PARI *)

Prog

(PARI) a290731(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); if(p==2, 2^(e-1), 1+p^(e+1)\(2*p+2)))} \\ from Andrew Howroyd
r=2; for(k=1, 40000, t=a290731(k)/k; if(t<r, r=t; print1(k, ", "))) \\ Hugo Pfoertner, Aug 23 2018

Crossrefs

Cf. A085635, A084848, A290728, A290731.

Sequence in context: A281703 A180216 A164302 * A190883 A284678 A367367

Adjacent sequences: A290724 A290725 A290726 * A290728 A290729 A290730

Keyword

nonn

Author

N. J. A. Sloane, Aug 10 2017

Extensions

More terms from Hugo Pfoertner, Aug 22 2018

Initial term added by Hugo Pfoertner, Aug 23 2018

Status

approved