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 A136115 Index m of least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists. 5

%I

%S 0,0,0,7,0,0,23,0,0,48,0,22,82,47,0,125,26,0,22,37,71,238,0,0,26,166,

%T 0,52,207,147,117,99,87,572,72,67,63,357,57,110,416,51,917,82,47,1050,

%U 217,380,167,246,0,97,697,0,374,191,537,1672,152,112,136,380,215,2037,68

%N Index m of 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)=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)=7 since P(7)=70 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(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 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)