cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A218794 Numbers that can be written as p^2 + 3pq + q^2 with primes p < q.

This page as a plain text file.
%I A218794 #9 Apr 08 2013 19:04:19
%S A218794 31,59,79,95,121,179,191,229,251,295,311,389,395,401,451,479,491,541,
%T A218794 569,671,695,719,745,809,899,971,1019,1061,1109,1111,1121,1151,1249,
%U A218794 1271,1301,1409,1451,1499,1595,1619,1661,1711,1919,1931,1949,1991,2059,2105,2111,2141,2195,2201,2245
%N A218794 Numbers that can be written as p^2 + 3pq + q^2 with primes p < q.
%C A218794 This is a subsequence of A218793, with the restriction that p < q, excluding terms of the form 5p^2 unless they would have another decomposition of the given form.
%C A218794 Sequence A218771 is the subsequence of primes in this sequence.
%e A218794 a(1) = 31 = p^2+3pq+q^2 for p=2, q=3.
%e A218794 a(20) = 671 = p^2+3pq+q^2 for (p,q)=(2,23) and (5,19) is the least term to allow more than 1 decomposition. See A218795 for more such terms.
%t A218794 With[{nn=60},Take[Union[#[[1]]^2+3Times@@#+#[[2]]^2&/@Subsets[Prime[ Range[ Floor[nn/3]]],{2}]],nn]] (* _Harvey P. Dale_, Apr 08 2013 *)
%o A218794 (PARI) is_A218794(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-1)\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}
%K A218794 nonn
%O A218794 1,1
%A A218794 _M. F. Hasler_, Nov 05 2012