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

Author

N. J. A. Sloane, Aug 10 2017

Keywords

• nonn

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.

Crossrefs

Cf. A085635, A084848, A290728, A290731.

Programs

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[tJean-François Alcover, Sep 03 2018, from PARI *)

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(tHugo Pfoertner, Aug 23 2018

Extensions

More terms from Hugo Pfoertner, Aug 22 2018

Initial term added by Hugo Pfoertner, Aug 23 2018