A390365 Numbers whose prime indices are not the first sums minus 1 of any multiset beginning with 1. Sorted list of all Heinz numbers of non-rows of A390308. Sorted complement of A390309.

9, 18, 25, 27, 35, 36, 45, 49, 50, 54, 63, 70, 72, 77, 81, 90, 91, 98, 99, 100, 108, 117, 121, 125, 126, 135, 140, 143, 144, 147, 153, 154, 162, 169, 171, 175, 180, 182, 187, 189, 196, 198, 200, 207, 209, 216, 221, 225, 234, 242, 243, 245, 247, 250, 252, 261

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

The prime indices of 25 are (3,3), which is not the first sums minus 1 of any multiset beginning with 1 (note (2,2,2) does not begin with 1), so 25 is in the sequence.
The prime indices of 39 are (2,6), which is the first sums minus 1 of (1,2,5), so 39 is not in the sequence.

Mathematica

nn=100;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
firsums[c_]:=Table[c[[i]]+c[[i+1]], {i, Length[c]-1}];
Complement[Range[nn], Table[Times@@Prime/@(firsums[Prepend[prix[n], 1]]-1), {n, Prime[nn]}]]

Crossrefs

This is the sorted version of the complement of A390309, triangle A390308.

The complement is A390364.

The non-prepended version is A390445, counted by A390447.

The non-prepended complement is A390448, counted by A390446.

The non-prepended non-sorted complement is A390449.

A112798 lists prime indices, sum A056239.

A243056 gives maximum prime index minus minimum prime index.

A358169 gives first differences plus one of 1-prepended prime indices, reverse A355534.

A390307 lists first sums of prime indices, for differences A355536.

Cf. A000040, A001222, A055396, A093641, A174090, A243055, A325351, A325352, A355531.

Sequence in context: A015798 A028494 A167663 * A347242 A038838 A347247

Adjacent sequences: A390362 A390363 A390364 * A390366 A390367 A390368

Keyword

nonn

Author

Gus Wiseman, Nov 21 2025

Status

approved