cp's OEIS Frontend

A235644 Number of decompositions of 12*n into the sum of two (not necessarily distinct) twin prime pairs.

%I A235644 #41 Jun 27 2014 13:14:52
%S A235644 0,1,1,2,1,2,1,2,1,2,1,2,2,2,2,0,2,1,3,3,1,2,1,3,2,2,2,3,1,3,1,2,3,3,
%T A235644 6,2,3,1,2,4,3,4,4,1,3,2,3,5,2,7,1,3,2,2,5,2,5,2,3,2,2,3,5,3,4,1,0,3,
%U A235644 1,6,2,3,3,1,5,2,5,3,3,4,1,4
%N A235644 Number of decompositions of 12*n into the sum of two (not necessarily distinct) twin prime pairs.
%C A235644 In the 1980's, Liang conjectured that (6n)^2 = p_1 + p_2 + p_3 + p_4, where (p_1, p_2) and (p_3, p_4) are twin prime pairs. See reference for more details.
%C A235644 It seems there are at least 2 solutions for the decompositions when n > 701.
%C A235644 If the two twin prime pairs are required to be distinct, the sequence is A187759.
%D A235644 Liang Ding Xiang, Problem 93#, Bulletin of Mathematics (Wuhan), 6(1992),41. ISSN 0488-7395.
%e A235644 a(736) = 2 because 12*736 = 197 + 199 + 4217 + 4219 = 857 + 859 + 3557 + 3559, so there are 2 ways of expressing 12*n as the sum of two twin prime pairs.
%o A235644 (PARI) v=select(p->isprime(p-2)&&p>5, primes(200))\6; l=List(); for(i=1, #v, if(2*v[i]<100, listput(l, 2*v[i])); for(j=i+1, #v, if((v[i]+v[j])<100, listput(l, v[i]+v[j])))); l1=vecsort(l); k=1; for(i=1, 100, s=sum(j=k, #l1, l1[j]==i); print1(s", "); k+=s) \\ _Lear Young_, Jun 16 2014
%o A235644 (PARI) v=select(p->isprime(p-2)&&p>5,primes(110))\6;for(i=1, 99, print1(sum(j=1,#v,vecsearch(v,i-v[j])>0 && i-v[j]>=v[j])", "))   \\ change i-v[j]>=v[j] to i-v[j]>v[j] is A187759.  _Lear Young_, Jun 16 2014
%Y A235644 Cf. A016910, A243941, A187759, A243914, A243956.
%K A235644 nonn
%O A235644 1,4
%A A235644 _Lear Young_, Jun 16 2014