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A332989 a(n) is the smallest number writable in n different ways as the sum of two distinct nonzero pentagonal numbers. 3

%I

%S 6,211,2999,13352,205427,250927,1134927,2177527,5002427,6422352,

%T 17349697,30135652,45997927,55075502,168570052,130917177,101275552,

%U 249483677,441561407,433742427,771789552,1546505052,1316582177,1701923302,2288827477,1073520852,3110207127

%N a(n) is the smallest number writable in n different ways as the sum of two distinct nonzero pentagonal numbers.

%C I conjecture this sequence is infinite.

%H Giovanni Resta, <a href="/A332989/b332989.txt">Table of n, a(n) for n = 1..40</a>

%e 211 can be written 35 + 176 and 1 + 210;

%e 2999 can be written 852 + 2147, 247 + 2752, 117 + 2882;

%e 13352 = P(52) + P(79) = P(29) + P(90) = P(17) + (93) = P(10) + P(94).

%o (PARI) a(n) = for(k=1, oo, if(sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5)==n, return(k))); \\ _Jinyuan Wang_, Mar 06 2020

%Y Cf. A000326, A332988.

%Y Cf. A093195 (analog sequence for perfect squares).

%K nonn

%O 1,1

%A _Olivier GĂ©rard_, Mar 05 2020

%E Name clarified by _Jinyuan Wang_, Mar 06 2020

%E Terms a(12) and beyond from _Giovanni Resta_, Mar 08 2020

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)