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

Author

Hartmut F. W. Hoft, Jun 10 2024

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000203, A237270, A351903.

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

Programs

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]