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 A267137 Numbers of the form x^2 + x + x*y + y + y^2 where x and y are integers. 3
 0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 14, 16, 17, 20, 21, 22, 24, 25, 26, 30, 32, 33, 34, 36, 37, 40, 41, 42, 44, 46, 49, 50, 52, 54, 56, 57, 58, 60, 64, 65, 66, 69, 70, 72, 74, 76, 80, 81, 82, 85, 86, 89, 90, 92, 94, 96, 97, 100, 101, 102, 104, 105, 108, 110, 112, 114, 116 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Inspired by relation between A003136 and A202822. See comment section of A202822. 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, ... Obviously, A000290, A002378 and A045944 are subsequences. The complement of this sequence is A322430. - Kemoneilwe Thabo Moseki, Dec 12 2019 LINKS 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. 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 Cf. A000290, A002378, A003136, A045944, A202822. Sequence in context: A277008 A091529 A184967 * A095775 A035063 A004128 Adjacent sequences:  A267134 A267135 A267136 * A267138 A267139 A267140 KEYWORD nonn AUTHOR Altug Alkan, Jan 10 2016 STATUS approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)