A359337 Irregular triangle read by rows: the n-th row gives the exponents of the powers of x corresponding to the maximal coefficient of the product x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

0, 2, 4, 5, 7, 12, 16, 17, 22, 24, 32, 42, 53, 65, 79, 96, 114, 134, 155, 180, 205, 233, 263, 294, 329, 364, 403, 442, 485, 529, 576, 625, 676, 729, 785, 842, 902, 964, 1029, 1097, 1167, 1238, 1313, 1390, 1469, 1552, 1636, 1723, 1813, 1904, 1999, 2096, 2195, 2298

Offset

0,2

Comments

Conjecture: except for n = 2, 5, and 6, the rows have length equal to 1.

Links

Table of n, a(n) for n=0..53.

Example

The irregular triangle begins:
    0;
    2;
    4, 5;
    7;
   12;
   16, 17;
   22, 24;
   32;
   42;
   53;
   65;
   ...

Mathematica

b[n_]:=CoefficientList[Product[Sum[x^Prime[i], {i, k}], {k, n}], x]; Table[Position[b[n], Max[b[n]]]-1, {n, 0, 50}]//Flatten

Crossrefs

Cf. A000040, A359328.

Cf. A359338 (minimal exponent), A359339 (maximal exponent).

Sequence in context: A165196 A007062 A121817 * A116432 A050027 A123643

Adjacent sequences: A359334 A359335 A359336 * A359338 A359339 A359340

Keyword

nonn,tabf

Author

Stefano Spezia, Dec 27 2022

Status

approved