A390361 Numbers k such that the first sums of 1-prepended prime indices of k are all distinct. Positions of strict rows in A390308.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 89, 90, 91, 93

Offset

1,2

Comments

First differs from A048103 in lacking 125.

First differs from A276078 in lacking 125.

First differs from A387181 in lacking 343.

First differs from A387576 in lacking 125.

The first sums of a sequence (a, b, c, d, ...) are (a+b, b+c, c+d, ...).

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=1..67.

Example

The prime indices of 10 are (1,3), 1-prepended (1,1,3), first sums (2,4), so 10 is in the sequence.
The prime indices of 12 are (1,1,2), 1-prepended (1,1,1,2), first sums (2,2,3), so 12 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}];
Join@@Position[Table[firsums[Prepend[prix[n], 1]]-1, {n, nn}], _?(UnsameQ@@#&)]

Crossrefs

The non-prepended version is A004709.

For differences instead of sums we have A325366, counted by A325349.

Positions of strict rows in A390308.

A112798 lists prime indices, sum A056239.

A243056 gives maximum prime index minus minimum prime index.

A358169 lists 1-prepended differences plus 1 of prime indices, reverse A355534.

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

A390309 ranks 1-prepended prime indices minus 1, union A390364, complement A390365.

Cf. A000040, A001222, A055396, A174090, A243055, A287352, A325328, A325351, A325390, A387181, A390363.

Sequence in context: A042968 A337037 A387576 * A048103 A276078 A387181

Adjacent sequences: A390358 A390359 A390360 * A390362 A390363 A390364

Keyword

nonn

Author

Gus Wiseman, Nov 07 2025

Status

approved