

A260261


Concatenation of their first digits yields the difference of two subsequent terms, a(1)=1. This is the lexicographically first infinite sequence with this property.


2



0, 1, 12, 24, 48, 97, 188, 199, 211, 233, 255, 277, 299, 322, 355, 388, 422, 466, 511, 566, 622, 688, 755, 833, 922, 1013, 1024, 1035, 1046, 1057, 1068, 1079, 1090, 1101, 1112, 1123, 1134, 1145, 1156, 1167, 1178, 1189, 1200, 1211, 1222, 1233, 1244, 1255, 1266, 1277
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OFFSET

0,3


COMMENTS

At each step, the smallest possible choice must be made for the next term.
The initial term a(0) = 0 has been added since it can be thought to make sense, but it is maybe not without controversy ("leading zero", unambiguous continuation, ...) and should therefore be considered as purely conventional or be ignored completely.
In contrast to A121805, this sequence is infinite.


LINKS

M. F. Hasler, Table of n, a(n) for n = 0..10000
E. Angelini, A story of leftmost digit (corrected), Jul 21 2015


FORMULA

a(10^7)=178567225.


EXAMPLE

a(1)=1 cannot be followed by a(2) = 2, 3, ..., 10 or 11 because this would yield concatenated first digits equal to 12, 13, ..., 19, 11 and 11, all different from the gap a(2)  a(1). But a(2) = 12 does produce a gap of 11 equal to the first two digits concatenated.
Then must follow a term >= 12 + 11 = 23 since the concatenation of the first two digits will be at least 11, but 23 would yield 12 for the concatenation, not equal to the gap. For a(3) = 24 the same concatenation is equal to the gap.
After a(25)=1013, and also after a(282)=10044, there follow many gaps of 11, then, e.g. after a(1187)=19999, one gap of 12 followed by about 450 gaps of 22, then one gap of 23 and about 300 gaps of 33, etc. After about 100 gaps of 99 the sequence reaches a(2850) = 99911, followed by a gap of 91, and then again more than 9000 gaps of 11.
This behavior will continue for each order of magnitude, so it is easily seen that the sequence is infinite.


PROG

(PARI) a=1; for(n=1, 100, print1(a", "); a+=10*digits(a)[1]; for(k=1, 9, digits(a+k)[1]==k&&(a+=k)&&next(2)); error) \\ The error never occurs.


CROSSREFS

Cf. A121805 (gap equals concatenation of the last and first digits, respectively).
Sequence in context: A270257 A180617 A081808 * A080495 A090776 A247944
Adjacent sequences: A260258 A260259 A260260 * A260262 A260263 A260264


KEYWORD

nonn,base


AUTHOR

Eric Angelini and M. F. Hasler, Jul 21 2015


STATUS

approved



