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A235644 Number of decompositions of 12*n into the sum of two (not necessarily distinct) twin prime pairs. 0
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, 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, 1, 6, 2, 3, 3, 1, 5, 2, 5, 3, 3, 4, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
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.
It seems there are at least 2 solutions for the decompositions when n > 701.
If the two twin prime pairs are required to be distinct, the sequence is A187759.
REFERENCES
Liang Ding Xiang, Problem 93#, Bulletin of Mathematics (Wuhan), 6(1992),41. ISSN 0488-7395.
LINKS
EXAMPLE
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.
PROG
(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
(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
CROSSREFS
Sequence in context: A033109 A321469 A365460 * A298475 A175096 A111627
KEYWORD
nonn
AUTHOR
Lear Young, Jun 16 2014
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)