A363872 Lexicographically earliest sequence of distinct terms > 0 such that n is a substring of a(n) + a(n+1).

1, 9, 3, 10, 4, 11, 5, 2, 6, 13, 87, 23, 89, 24, 90, 25, 91, 26, 92, 27, 93, 28, 94, 29, 95, 30, 96, 31, 97, 32, 98, 33, 99, 34, 100, 35, 101, 36, 102, 37, 103, 38, 104, 39, 105, 40, 106, 41, 7, 42, 8, 43, 109, 44, 110, 45, 111, 46, 12, 47, 113, 48, 14, 49, 15

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Eric Angelini, Échecs et Maths, Personal blog, bottom of page.

Example

n = 1 is a substring of the sum  1 +  9 = 10
n = 2 is a substring of the sum  9 +  3 = 12
n = 3 is a substring of the sum  3 + 10 = 13
n = 4 is a substring of the sum 10 +  4 = 14
n = 5 is a substring of the sum  4 + 11 = 15
n = 6 is a substring of the sum 11 +  5 = 16
...
n = 10 is a substring of the sum 13 + 87 = 100, etc.

Maple

R:= 1: x:= 1: S:= {1}:
for n from 1 to 100 do
  ns:= convert(n, string);
  for y from 1 do
    if member(y, S) then next fi;
    if SearchText(ns, convert(x+y, string)) <> 0 then
      R:= R, y; x:= y; S:= S union {y}; break
    fi
  od
od:
R;  # Robert Israel, Jul 04 2023

Mathematica

a[1] = 1; a[n_] := a[n] = Module[{k = 2}, While[! FreeQ[Array[a, n - 1], k] || ! StringContainsQ[ToString[a[n - 1] + k], ToString[n - 1]], k++]; k]; Array[a, 100] (* Amiram Eldar, Jul 04 2023 *)

Crossrefs

Cf. A299952.

Sequence in context: A361062 A003565 A238105 * A166203 A248312 A329653

Adjacent sequences: A363869 A363870 A363871 * A363873 A363874 A363875

Keyword

base,nonn

Author

Eric Angelini, Jul 03 2023

Status

approved