

A277268


If we call "T" this sequence and consider the kdigit term a(n) of T with digits abcd...k, then a(n+1) = [a(n) + the ath digit of T + the bth digit of T + the cth digit of T + ... + the kth digit of T]. This is the lexicographically first such infinite sequence containing no duplicate term.


2



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
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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: A228709 A292513 A171491 * A337254 A152200 A277694
Adjacent sequences: A277265 A277266 A277267 * A277269 A277270 A277271


KEYWORD

nonn,base


AUTHOR

Eric Angelini and JeanMarc Falcoz, Nov 07 2016


STATUS

approved



