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

1,1

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.

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 *)

Prog

(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

Crossrefs

Cf. A338038, A338039.

Sequence in context: A058954 A205258 A255732 * A353807 A326236 A156636

Adjacent sequences: A338163 A338164 A338165 * A338167 A338168 A338169

Keyword

nonn,base

Author

Michel Marcus, Oct 14 2020

Status

approved