A339138 Lexicographically earliest sequence of distinct nonnegative terms such that the first digit d of a(n), for n > 1, is the sum of the two closest digits of d (they are the rightmost digit of a(n-1) and the next digit on the right of d).

0, 1, 10, 2, 20, 3, 30, 4, 40, 5, 50, 6, 60, 7, 70, 8, 80, 9, 90, 11, 21, 32, 31, 43, 41, 54, 51, 65, 61, 76, 71, 87, 81, 98, 91, 100, 22, 42, 53, 52, 64, 62, 75, 72, 86, 82, 97, 92, 200, 33, 63, 74, 73, 85, 83, 96, 93, 300, 44, 84, 95, 94, 400, 55, 500, 66

Offset

1,3

Comments

The first two digits of a(n) cannot be in ascending order.

Links

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

Example

a(2) = 1 and 1 is the sum of 0 + 1 (closest digits to 1);
a(3) = 10 and 1 is the sum of 1 + 0 (closest digits to 1);
a(4) = 2 and 2 is the sum of 0 + 2 (closest digits to 2);
a(5) = 20 and 2 is the sum of 2 + 0 (closest digits to 2); etc.

Prog

(Python)
a, d = [0], 1
while len(a) < 66:
    if d < 10 and a[-1] % 10 == 0: a.append(d); d += 1
    k = 10
    while k in a or (a[-1]%10) + int(str(k)[1]) != int(str(k)[0]): k += 1
    a.append(k)
print(a) # Dominic McCarty, Jun 15 2025

Crossrefs

Cf. A339139 (where the last digit is involved, instead of the first digit).

Sequence in context: A330365 A173237 A319154 * A086068 A262557 A030595

Adjacent sequences: A339135 A339136 A339137 * A339139 A339140 A339141

Keyword

base,nonn

Author

Eric Angelini, Nov 25 2020

Extensions

Corrected and extended by Dominic McCarty, Jun 15 2025

Status

approved