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 A270122 Indices of prime numbers of the form x^2 + x + x*y + y + y^2 where x and y are integers. 0
 1, 3, 7, 12, 13, 24, 25, 26, 33, 35, 45, 50, 51, 53, 55, 59, 60, 77, 79, 80, 82, 84, 87, 88, 104, 106, 113, 116, 121, 123, 127, 135, 136, 140, 148, 152, 159, 165, 169, 174, 176, 178, 184, 186, 189, 204, 209, 211, 212, 216, 218, 221, 223, 226, 227, 237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS How is the distribution of a(n), a(n+1) in this sequence where a(n+1) = a(n) + 1? LINKS EXAMPLE 1 is a term because prime(1) = 2 = (-2)^2 + (-2) + (-2)*1 + 1 + 1^2. 3 is a term because prime(3) = 5 = 1^2 + 1 + 1*1 + 1 + 1^2. 7 is a term because prime(7) = 17 = (-5)^2 + (-5) + (-5)*3 + 3 + 3^2. 12 is a term because prime(12) = 37 = (-7)^2 + (-7) + (-7)*5 + 5 + 5^2. 13 is a term because prime(13) = 41 = 7^2 + 7 + 7*(-3) + (-3) + (-3)^2. PROG (PARI) isA003136(n) = #bnfisintnorm(bnfinit(z^2+z+1), n); for(n=1, 250, if(isA003136(3*prime(n)+1), print1(n, ", "))); CROSSREFS Cf. A000040, A003136, A267137. Sequence in context: A215631 A081695 A290955 * A142958 A310214 A310215 Adjacent sequences:  A270119 A270120 A270121 * A270123 A270124 A270125 KEYWORD nonn AUTHOR Altug Alkan, Mar 11 2016 STATUS approved

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Last modified April 18 07:59 EDT 2021. Contains 343084 sequences. (Running on oeis4.)