A373609 List of repeated terms in A351903.

45, 135, 225, 315, 405, 675, 945, 1035, 1125, 1155, 1215, 1305, 1365, 1485, 1575, 1755, 2079, 2275, 2475, 2565, 2835, 3105, 3375, 3465, 3825, 3915, 4095, 4275, 4550, 4725, 5175, 5265, 5355, 5625, 5775, 5985, 6050, 6237, 6370, 6525, 6615, 6650, 6825, 6885, 6975, 7245, 7315, 7425

Offset

1,1

Comments

It appears that all repeated terms in A351903 occur in pairs only, and either are odd or multiples of 10; true through a(4543) = 999999.

It is not known whether this sequence is infinite. A351903 is infinite, but not increasing.

Links

Table of n, a(n) for n=1..48.

Example

a(1) = 45 = A351903(23) = A351903(32) and A237270[45] = {23, 32, 23}.
a(2) = 135 = A351903(68) = A351903(104) and A237270[135] = {68, 104, 68}.
a(17) = 2079 = A351903(1040) = A351903(1064) and A237270[2079] = {1040, 348, 1064, 348, 1040} is the smallest number in this sequence whose symmetric representation of sigma has 5 parts.
a(137) = 22365 = A351903(11183) = A351903(11281) and A237270[22365] = {11183, 11281, 11281, 11183} is the smallest number in this sequence whose symmetric representation of sigma has 4 parts.

Mathematica

(* function a237270[ ] and its support functions are defined in A351903 *)
a373609[n_] := Module[{pL={}, rL={}, k, a, j, c}, For[k=1, k<=n, k++, a=a237270[k]; c=0; For[j=1, j<=Length[a], j++, If[!MemberQ[pL, a[[j]]], AppendTo[pL, a[[j]]]; c++]]; If[c>1, AppendTo[rL, k]]]; rL]
a373609[7425]

Crossrefs

Cf. A000203, A237270, A351903.

See A237593 for more comprehensive cross-references re symmetric representation of sigma.

Sequence in context: A098924 A195318 A131011 * A336507 A156370 A044377

Adjacent sequences: A373606 A373607 A373608 * A373610 A373611 A373612

Keyword

nonn

Author

Hartmut F. W. Hoft, Jun 10 2024

Status

approved