

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
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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

Table of n, a(n) for n=1..56.


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



