A339139 Lexicographically earliest sequence of distinct nonnegative terms such that the last digit d of a(n), for n > 1, is the sum of the two closest digits of d (they are the leftmost digit of a(n+1) and the digit on the left of d).

1, 2, 12, 13, 23, 14, 34, 15, 45, 16, 56, 17, 67, 18, 78, 19, 89, 101, 102, 24, 25, 35, 26, 46, 27, 57, 28, 68, 29, 79, 201, 103, 36, 37, 47, 38, 58, 39, 69, 301, 104, 48, 49, 59, 401, 105, 501, 106, 601, 107, 701, 108, 801, 109, 901, 112, 113, 202, 203, 302, 204, 402, 205, 502, 206, 602, 207, 702, 208, 802, 209, 902

Offset

1,2

Comments

The last two digits of a(n) must be in ascending order (thus no term of the sequence ends in 0).

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Example

a(2) = 2 and 2 is the sum of 1 + 1 (closest digits to 2);
a(3) = 12 and 2 is the sum of 1 + 1 (closest digits to 2);
a(4) = 13 and 3 is the sum of 1 + 2 (closest digits to 3);
a(5) = 23 and 3 is the sum of 2 + 1 (closest digits to 3); etc.

Prog

(Python)
a = [1, 2, 12]
while len(a) < 72:
    l = int(str(a[-1])[-1])-int(str(a[-1])[-2])
    k = 10 * l
    while k in a or k % 10 == 0 or int(str(k)[-1]) <= int(str(k)[-2]): k = k+1 if int(str(k+1)[0]) == l else l * (10 ** (len(str(k-1))))
    a.append(k)
print(a) # Dominic McCarty, Jun 14 2025

Crossrefs

Cf. A339138 (where the first digit is involved, instead of the last digit)

Sequence in context: A182271 A178362 A299961 * A143795 A032931 A072483

Adjacent sequences: A339136 A339137 A339138 * A339140 A339141 A339142

Keyword

base,nonn

Author

Eric Angelini, Nov 25 2020

Status

approved