OFFSET
1,3
COMMENTS
Prime terms of this sequence are 2, 5, 17, 37, 41, 89, 97, 101, 137, 149, ...
Perfect power terms of this sequence are 1, 4, 8, 9, 16, 25, 32, 36, 49, 64, 81, 100, 121, 144, 169, ...
The complement of this sequence is A322430. - Kemoneilwe Thabo Moseki, Dec 12 2019
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10583
Alexandre Chaduteau, Nyan Raess, Henry Davenport, and Frank Schindler, Hilbert Space Fragmentation in the Chiral Luttinger Liquid, arXiv:2409.10359 [cond-mat.str-el], 2024. See pp. 5, 8.
FORMULA
a(n) = (A202822(n) - 1) / 3.
EXAMPLE
1 is a term because (-1)^2 + (-1) + (-1)*(-1) + (-1) + (-1)^2 = 1.
4 is a term because 2^2 + 2 + 2*(-2) + (-2) + (-2)^2 = 4.
24 is a term because 2^2 + 2 + 2*3 + 3 + 3^2 = 24.
MATHEMATICA
f[{i_, j_}] := (i^2 + i*j + j^2 + i + j); Union@ Map[f, Tuples[Range[-10, 10], 2] ] (* Michael De Vlieger, Sep 23 2024, after Harvey P. Dale at A202822 *)
PROG
(PARI) x='x+O('x^500); p=eta(x)^3/eta(x^3); for(n=0, 499, if(polcoeff(p, n) != 0 && n%3==1, print1((n-1)/3, ", ")));
(PARI) is(n) = sumdiv( n, d, kronecker( -3, d));
for(n=0, 1e3, if(is(3*n+1), print1(n, ", ")));
(PARI) is(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
for(n=0, 1e3, if(is(3*n+1), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 10 2016
STATUS
approved