A341037 The successive remainders of the division by (a(n) + a(n+1)) of concat(a(n),a(n+1)) rebuild the sequence itself.

1, 3, 5, 30, 12, 4, 10, 6, 2, 26, 23, 75, 72, 40, 16, 33, 44, 54, 93, 406, 592, 4407, 5591, 44408, 55590, 4398, 5600, 44399, 55599, 94398, 393325, 106674, 8303, 1695, 800, 198, 96, 51, 47, 452, 546, 42, 56, 8, 20, 15, 9, 89, 410, 80, 18, 24, 25, 45, 53, 446

Offset

1,2

Comments

Lexicographically earliest sequence of distinct terms > 0 with this property.

The sequence is conjectured to be a permutation of the integers > 0.

Links

Table of n, a(n) for n=1..56.

Example

   1 and 3  ->   13/4  with remainder  1
   3 and 5  ->   35/8  with remainder  3
   5 and 30 ->  530/35 with remainder  5
  30 and 12 -> 3012/42 with remainder 30
  12 and 4  ->  124/16 with remainder 12
   4 and 10 ->  410/14 with remainder  4
  10 and 6  ->  106/16 with remainder 10
   6 and 2  ->   62/8  with remainder  6; etc.
The first and last column are identical.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[Array[a, n-1], k]||Mod[FromDigits@Flatten[IntegerDigits/@{a[n-1], k}], a[n-1]+k]!=a[n-1], k++]; k]; Array[a, 27] (* Giorgos Kalogeropoulos, May 11 2022 *)

Prog

(PARI) lista(nn) = {my(k, v=vector(nn)); v[1]=1; for(i=1, nn-1, k=1; until(eval(Str(v[i], k))%(v[i]+k)==v[i]&&!vecsearch(vecsort(v), k), k++); v[i+1]=k); v; } \\ Jinyuan Wang, Feb 10 2021

Crossrefs

Cf. A095245.

Sequence in context: A100858 A215780 A214655 * A181429 A162262 A151373

Adjacent sequences: A341034 A341035 A341036 * A341038 A341039 A341040

Keyword

nonn,base

Author

Eric Angelini, Feb 03 2021

Extensions

More terms from Jinyuan Wang, Feb 10 2021

Status

approved