OFFSET
1,2
COMMENTS
A subsequence of A136113, obtained by omitting A136113(A135771(k)), k=1,2,3,... ; i.e. those which are not the difference of two larger pentagonal numbers, but the difference of a larger and a smaller pentagonal number.
The definition ("...two other...") excludes the case P(n) = P(m)-P(n), cf. comment by R. J. Mathar in A000326.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..200
FORMULA
P(n)=n*(3*n-1)/2 <=> n*(n-1/3) = (2/3)*P(n), thus m = P(n) <=> m = P([sqrt(2m/3)]+1)
and m = P(n) <=> 24m+1 = (6n-1)^2, useful for investigating the possibility of writing P(n)=P(n')+P(n"): this is possible whenever (6n-1)^2=(6n'-1)^2+(6n"-1)^2-1.
PROG
(PARI) P(n)=n*(3*n-1)/2
isPent(t)=P(sqrtint((t*2)\3)+1)==t
for( i=1, 999, for( j=1, (P(i)-1)\3, isPent(P(i)+P(j))&j!=i&next(2)); print1(P(i)", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar and M. F. Hasler, Feb 07 2008
STATUS
approved