A290729 Analog of A085635, replacing "quadratic residue" (X^2) with "value of X(3X-1)/2".

1, 5, 7, 11, 13, 17, 19, 23, 25, 35, 55, 65, 77, 91, 119, 133, 143, 175, 275, 325, 385, 455, 595, 665, 715, 935, 1001, 1309, 1463, 1547, 1729, 1925, 2275, 2975, 3325, 3575, 4675, 5005, 6545, 7315, 7735, 8645

Offset: 1

Author

N. J. A. Sloane, Aug 10 2017

Keywords

• nonn

Comments

Positions k where R(k) = A290732(k)/k, achieves a new minimum.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..182
• Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. See Table 6.

Crossrefs

Cf. A000326, A085635, A084848, A290727, A290728, A290730, A290732.

Programs

Mathematica

a[n_] := Product[{p, e} = pe; If[p <= 3, p^e, (p^e - p^(e-1))/2 + (p^(e-1) - p^(Mod[e+1, 2]))/(2*(p+1)) + 1], {pe, FactorInteger[n]}];
r = 2; Reap[For[j=1, j <= 10^4, j = j+1, t = a[j]/j; If[tJean-François Alcover, Oct 02 2018, after Hugo Pfoertner *)

PARI

a290732(n)={my(f=factor(n));prod(k=1,#f~,my([p,e]=f[k,]);if(p<=3,p^e,(p^e-p^(e-1))/2+(p^(e-1)-p^((e+1)%2))/(2*(p+1))+1))}
my(r=2);for(j=1,10001,my(t=a290732(j)/j);if(tHugo Pfoertner, Aug 26 2018

Extensions

a(1) corrected by Hugo Pfoertner, Aug 26 2018