Vincenzo Manto

A395817

Created: 5/22/2026 | Author: Vincenzo Manto and James C. McMahon , May 07 2026

Strictly increasing minimal sequence where consecutive terms can be added digit-by-digit without carrying in base 10.

Many integers (e.g., 6, 7, 8, 9, 15, 16...) are never present because the greedy behavior and the strictly increasing condition bypass them to avoid carries.A subset of nonnegative integers with no decimal digits > 5 (A007092).

Sequence Chart

Graph of A395817

Data

1,2,3,4,5,10,11,12,13,14,15,20,21,22,23,24,25,30,31,32,33,34,35,40,41,42,43,44,45,50,100,101,102,103,104,105,110,111,112,113,114,115,120,121,122,123,124,125,130,131,132,133,134,135,140,141,142,143,144

Formula

a(1)=1; a(n) = min { x > a(n-1) | d_i(x) + d_i(a(n-1)) <= 9 }.

Computational Implementations

PYTHON

def has_carry(a, b):
    while a or b:
        if (a % 10) + (b % 10) > 9:
            return True
        a //= 10; b //= 10
    return False
def sequence(n):
    terms = [1]
    while len(terms) < n:
        k = terms[-1] + 1
        while has_carry(terms[-1], k):
            k += 1
        terms.append(k)
    return terms

Mathematica

s={1};k=2;Do[While[Max[IntegerDigits[k]]>5||Max[IntegerDigits[s[[-1]]]+Take[IntegerDigits[k],-IntegerLength[s[[-1]]]]]> 9,k++];AppendTo[s,k];k++,{i,58}];s

Cross-References

See also OEIS entries: Cf. A052413, A007092.