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 A136114 Least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists. 4

%I

%S 0,0,0,70,0,0,782,0,0,3432,0,715,10045,3290,0,23375,1001,0,715,2035,

%T 7526,84847,0,0,1001,41251,0,4030,64170,32340,20475,14652,11310,

%U 490490,7740,6700,5922,190995,4845,18095,259376,3876,1260875,10045,3290

%N Least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists.

%F a(n)=A000326(A136115(n)). a(n)=0 iff n is in A136112 iff A000326(n) is in A136113.

%e a(1..3)=0 since P(1),P(2),P(3) cannot be written as difference of 2 other pentagonal numbers > 0.

%e a(4)=70=P(7) is the least pentagonal number > P(4)=22 such that their sum is again a pentagonal number, P(8).

%o (PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */ /* newline */ isPent(t)=P(sqrtint(t<<1\3)+1)==t /* newline */ for( i=1,99,for( j=i+1,(P(i)-1)\3, isPent(P(i)+P(j))&print1(P(j)",")|next(2));print1(0","))

%Y Cf. A000326, A136112-A136118.

%K nonn

%O 1,4

%A _M. F. Hasler_, Dec 15 2007

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Last modified September 26 15:09 EDT 2022. Contains 357000 sequences. (Running on oeis4.)