A367363 First term is 1; thereafter, if u and v are consecutive terms, with decimal expansions u = bc...ef, v = hi...jk, then v-u has decimal expansion efhi, formed by concatenating the last two digits of u and the first two digits of v. If there is a choice for v, pick the smallest.

1, 112, 1325, 3863, 10173, 17490, 26516, 28144, 32576, 40216, 41857, 47604, 48052, 53305, 53858, 59717, 61478, 69347, 74121, 76297, 86083, 94477, 102187, 110898, 120710, 121722, 123934, 127346, 131959, 137872, 145086, 153701, 153816, 155431, 158546, 163162

Offset

1,2

Comments

A generalization of A121805.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(1) = 1, so ef = "01" = 1. So v-u will be a four-digit number (with a leading zero in this case), say v-u = 0xyz, with v = 1 + xyz. This suggests that we try x=1 and y=1, v = 1 + xyz = 1 + 11*, where * = 1+z. The smallest choice is z = 0, giving "efhi" = "0111" = 111, and a(2) = 1 + 111 = 112 works.

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, y = 1, 1
    while y:
        yield an
        an, y = an + 100*(an%100), 1
        y = next((y for y in range(1, 100) if str(an+y)[:2] == str(y)), 0)
        an += y
print(list(islice(agen(), 36))) # Michael S. Branicky, Nov 23 2023

Crossrefs

Cf. A121805.

Sequence in context: A233115 A188152 A353782 * A327633 A210300 A210293

Adjacent sequences: A367360 A367361 A367362 * A367364 A367365 A367366

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 23 2023

Extensions

More terms from Michael S. Branicky, Nov 23 2023

Status

approved