A338166 Terms of A338039 that are repeated concatenations of smaller integers.

1818, 8181, 181818, 198198, 405405, 484848, 504504, 565656, 576576, 656565, 675675, 818181, 848484, 891891, 11311131, 13041304, 13111311, 18181818, 19981998, 22622262, 26222622, 33933393, 39333933, 40314031, 41544154, 45144514, 46364636, 63646364, 81818181, 87498749, 89918991, 94789478

Offset: 1

Author

Michel Marcus, Oct 14 2020

Keywords

• nonn
• base

Links

• Michel Marcus, Table of n, a(n) for n = 1..1050 (up to 15 digits).
• Daniel Tsai, A recurring pattern in natural numbers of a certain property, arXiv:2010.03151 [math.NT], 2020.
• Daniel Tsai, A recurring pattern in natural numbers of a certain property, Integers (2021) Vol. 21, Article #A32.

Crossrefs

Cf. A338038, A338039.

Programs

Mathematica

Block[{f}, f[1] = 0; f[n_] := Plus @@ #[[All, 1]] + Plus @@ Select[#[[All, -1]], # > 1 &] &@ FactorInteger[n]; Select[Union@ Flatten@ Table[Union@ Flatten@ Map[Function[k, Map[FromDigits[Join @@ ConstantArray[IntegerDigits[#], n/k]] &, Range[10^(k - 1), 10^k - 1]]], Most@ Divisors[n]], {n, 3, 8}], And[Mod[#1, 10] != 0, #2 != #1, f[#1] == f[#2]] & @@ {#, IntegerReverse[#]} &] ] (* Michael De Vlieger, May 27 2021, after Amiram Eldar at A338039 *)

PARI

f(n) = my(f=factor(n)); vecsum(f[,1]) + sum(k=1, #f~, if (f[k,2]!=1, f[k,2])); \\ A338038
isok(m) = my(r=fromdigits(Vecrev(digits(m)))); if ((r != m) && (f(r) == f(m)), return(m));
listc(c) = {my(list = List()); fordiv(c, d, if ((d != 1) && (d != c), for(k=10^(d-1), 10^d, if (k % 10, my(sk = Str(k), skk = sk); for (j=1, c/d-1, sk = concat(sk, skk)); if (isok(eval(sk)), listput(list, eval(sk))););););); list;}
lista(nn) = {my(list = List()); forcomposite(c=1, nn, my(clist = Vec(listc(c))); for (k=1, #clist, listput(list, clist[k]));); vecsort(Vec(list),,8);}
lista(8) \\ to get terms up to 8 digits