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List of repeated terms in A351903.
1

%I #32 Jul 13 2024 00:22:59

%S 45,135,225,315,405,675,945,1035,1125,1155,1215,1305,1365,1485,1575,

%T 1755,2079,2275,2475,2565,2835,3105,3375,3465,3825,3915,4095,4275,

%U 4550,4725,5175,5265,5355,5625,5775,5985,6050,6237,6370,6525,6615,6650,6825,6885,6975,7245,7315,7425

%N List of repeated terms in A351903.

%C 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.

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

%e a(1) = 45 = A351903(23) = A351903(32) and A237270[45] = {23, 32, 23}.

%e a(2) = 135 = A351903(68) = A351903(104) and A237270[135] = {68, 104, 68}.

%e 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.

%e 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.

%t (* function a237270[ ] and its support functions are defined in A351903 *)

%t 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]

%t a373609[7425]

%Y Cf. A000203, A237270, A351903.

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

%K nonn

%O 1,1

%A _Hartmut F. W. Hoft_, Jun 10 2024