cp's OEIS Frontend

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)).

%I A359337 #11 Dec 31 2022 15:18:15
%S A359337 0,2,4,5,7,12,16,17,22,24,32,42,53,65,79,96,114,134,155,180,205,233,
%T A359337 263,294,329,364,403,442,485,529,576,625,676,729,785,842,902,964,1029,
%U A359337 1097,1167,1238,1313,1390,1469,1552,1636,1723,1813,1904,1999,2096,2195,2298
%N 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)).
%C A359337 Conjecture: except for n = 2, 5, and 6, the rows have length equal to 1.
%e A359337 The irregular triangle begins:
%e A359337     0;
%e A359337     2;
%e A359337     4, 5;
%e A359337     7;
%e A359337    12;
%e A359337    16, 17;
%e A359337    22, 24;
%e A359337    32;
%e A359337    42;
%e A359337    53;
%e A359337    65;
%e A359337    ...
%t A359337 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
%Y A359337 Cf. A000040, A359328.
%Y A359337 Cf. A359338 (minimal exponent), A359339 (maximal exponent).
%K A359337 nonn,tabf
%O A359337 0,2
%A A359337 _Stefano Spezia_, Dec 27 2022