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A218793 Numbers that can be written as p^2 + 3pq + q^2 with prime p and q. 2
20, 31, 45, 59, 79, 95, 121, 125, 179, 191, 229, 245, 251, 295, 311, 389, 395, 401, 451, 479, 491, 541, 569, 605, 671, 695, 719, 745, 809, 845, 899, 971, 1019, 1061, 1109, 1111, 1121, 1151, 1249, 1271, 1301, 1409, 1445, 1451, 1499, 1595, 1619, 1661, 1711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence A218771 is the subsequence of primes in this sequence.

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..7196 (all terms below 10^6).

EXAMPLE

a(1) = 20 = p^2+3pq+q^2 for p=q=2, in the same way all numbers of the form 5p^2 are member of the sequence.

a(2) = 31 = p^2+3pq+q^2 for p=2, q=3.

a(25) = 671 = p^2+3pq+q^2 for (p,q)=(2,23) and (5,19), is the least term to allow more than 1 decomposition.

a(1431) = 136895 = p^2+3pq+q^2 for (p,q)=(2,367), (67,277) and (103,233), is the least term to allow more than 2 decompositions.

MATHEMATICA

nf[{a_, b_}]:=a^2+3a*b+b^2; Take[Union[nf/@Tuples[Prime[Range[20]], 2]], 50] (* Harvey P. Dale, Mar 31 2015 *)

PROG

(PARI) is_A218793(n, v=0)={ /* set v=1 to count number of decompositions, and v=2 to print them */ my(r, c=0); forprime( q=1, sqrtint(n\5), issquare(4*n+5*q^2, &r) || next; isprime((r-3*q)/2) || next; v || return(1); v>1 & print1([q, (r-3*q)/2]", "); c++); c}

CROSSREFS

Sequence in context: A158844 A077340 A077343 * A116131 A212050 A075035

Adjacent sequences:  A218790 A218791 A218792 * A218794 A218795 A218796

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 05 2012

STATUS

approved

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Last modified February 29 08:26 EST 2020. Contains 332355 sequences. (Running on oeis4.)