A347353 Lexicographically earliest sequence of distinct positive terms such that the rightmost digit of a(n) concatenated with the leftmost digit of a(n+1) form an integer that is the sum of the digits of a(n) and a(n+1).

1, 19, 1899999999, 29, 1799999999, 119, 1889999999, 128, 169999999, 1299, 178999999, 1389, 179899999, 1398, 15999999, 13999, 16899999, 14899, 16989999, 14989, 16998999, 14998, 1499999, 149999, 1589999, 158999, 1598999, 159899, 1599899, 159989, 1599989, 159998, 139999, 1599999, 148999

Offset

1,2

Comments

In other words, the two digits squeezing a comma form the sum of the digits of the two terms squeezing the comma. This sequence is finite and has 1309 terms, the last one being 191.

Links

Table of n, a(n) for n=1..35.

Example

a(1), a(2) = 1, 19 and 11 is 1 + (1+9);
a(2), a(3) = 19, 1899999999 and 91 is (1+9) + (1+8+9+9+9+9+9+9+9+9);
a(3), a(4) = 1899999999, 29 and 92 is (1+8+9+9+9+9+9+9+9+9) + (9+2);
a(4), a(5) = 29, 1799999999 and 91 is (2+9) + (1+7+9+9+9+9+9+9+9+9); etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(t=1; While[!IntegerQ[m=Min@Union@Flatten@Table[l=FromDigits[{Last[s=IntegerDigits@a[n-1]], k}]-Total@s; Complement[FromDigits/@Flatten[Permutations/@Select[Sort/@IntegerPartitions[l, t, Range@9], First@#==k&], 1], Array[a, n-1]], {k, 9}]], t++]; m); Array[a, 35] (* Giorgos Kalogeropoulos, May 05 2022 *)

Crossrefs

Cf. A121805, A139284.

Sequence in context: A087515 A038028 A013890 * A128400 A211378 A133591

Adjacent sequences: A347350 A347351 A347352 * A347354 A347355 A347356

Keyword

base,nonn,fini

Author

Eric Angelini and Carole Dubois, Aug 28 2021

Status

approved