A277268 If we call "T" this sequence and consider the k-digit term a(n) of T with digits abcd...k, then a(n+1) = [a(n) + the a-th digit of T + the b-th digit of T + the c-th digit of T + ... + the k-th digit of T]. This is the lexicographically first such infinite sequence containing no duplicate term.

11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 45, 49, 53, 55, 57, 59, 61, 67, 73, 75, 77, 79, 81, 89, 97, 99, 101, 103, 105, 107, 109, 111, 114, 119, 122, 125, 128, 137, 140, 144, 151, 154, 159, 162, 169, 176, 183, 192, 195, 198, 207, 209, 211, 214, 219, 222, 225, 228, 237, 240, 244, 251, 254, 259, 262, 269, 276, 283, 292, 295, 298, 307

Offset

1,1

Comments

There are 3 lexicographically earlier sequences with this property, but they all stop at some point. The first one is A276514, starting with 5,10,15,25,31,... and halting with a(49) = 300. The second one starts with 9,10,19,29,31,... and stops with a(246) = 3003. The third one starts with 10,11,13,15,17,... and ends with a(8) = 22, as shown here: 10, 11, 13, 15, 17, 19, 21, 22. [To compute a hypothetical a(9), one has to add to 22 the second digit of the sequence (which is zero) and (again) the second digit of the sequence (again zero): 22+0+0 = 22.]

As this sequence, starting with 11, 13, 15, 17, 19, ..., shows no zero digit among its first 10 digits, it will never stop.

Links

Eric Angelini, Table of n, a(n) for n = 1..1001

Example

To compute a(2), add to a(1) the 1st digit of T and the 1st digit of T, so a(2) = 11+1+1 = 13;
to compute a(3), add to a(2) the 1st digit of T and the 3rd digit of T, so a(3) = 13+1+1 = 15;
to compute a(4), add to a(3) the 1st digit of T and the 5th digit of T, so a(4) = 15+1+1 = 17;
to compute a(5), add to a(4) the 1st digit of T and the 7th digit of T, so a(5) = 17+1+1 = 19;
to compute a(6), add to a(5) the 1st digit of T and the 9th digit of T, so a(6) = 19+1+1 = 21;
to compute a(7), add to a(6) the 2nd digit of T and the 1st digit of T, so a(7) = 19+1+1 = 23;
etc.

Crossrefs

Cf. A276514.

Sequence in context: A358076 A292513 A171491 * A337254 A152200 A277694

Adjacent sequences: A277265 A277266 A277267 * A277269 A277270 A277271

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Nov 07 2016

Status

approved