A351840 Lexicographically earliest infinite sequence of distinct positive integers such that a(1) = 1 and a(n-1) + a(n) is divisible by the first digit of a(n).

1, 10, 2, 11, 12, 3, 13, 14, 7, 15, 5, 16, 4, 17, 18, 6, 19, 21, 23, 25, 27, 9, 29, 31, 32, 8, 20, 22, 24, 26, 28, 35, 34, 38, 37, 43, 41, 47, 45, 30, 33, 36, 39, 49, 51, 54, 42, 46, 59, 56, 40, 44, 48, 52, 53, 57, 58, 62, 64, 68, 72, 60, 50, 55, 65, 61, 79, 75, 63, 69, 71, 67, 73, 74, 86, 82, 98, 70

Offset

1,2

Comments

This sequence is a permutation of the positive integers.

First differs from A323821 at a(32).

Links

Carole Dubois, Table of n, a(n) for n = 1..200

Index entries for sequences that are permutations of the natural numbers

Example

a(1) + a(2) = 1 + 10 = 11 which is divisible by 1 (the first digit of 10);
a(2) + a(3) = 10 + 2 = 12 which is divisible by 2 (the first digit of 2);
a(3) + a(4) = 2 + 11 = 13 which is divisible by 1 (the first digit of 11);
a(4) + a(5) = 11 + 12 = 23 which is divisible by 1 (the first digit of 12);
a(5) + a(6) = 12 + 3 = 15 which is divisible by 3 (the first digit of 3); etc.

Mathematica

nn = 78; c[_] = 0; a[1] = c[1] = u = 1; Do[While[c[u] != 0, u++]; k = u; While[Nand[c[k] == 0, Mod[a[n - 1] + k, First@ IntegerDigits[k]] == 0], k++]; Set[{a[n], c[k]}, {k, n}], {n, 2, nn}]; Array[a[#] &, nn] (* Michael De Vlieger, Feb 21 2022 *)

Prog

(Python)
def aupton(terms):
    alst, aset, minunused = [1], {1}, 2
    while len(alst) < terms:
        an = minunused
        while an in aset or (alst[-1]+an)%int(str(an)[0]): an += 1
        alst.append(an); aset.add(an)
        while minunused in aset: minunused += 1
    return alst
print(aupton(100)) # Michael S. Branicky, Feb 21 2022

Crossrefs

Cf. A323821.

Sequence in context: A293869 A365625 A323821 * A257277 A248024 A269631

Adjacent sequences: A351837 A351838 A351839 * A351841 A351842 A351843

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 21 2022

Status

approved