Vincenzo Manto

A395817

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

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

This sequence has been cited by and influenced 1 other sequence

Official Comments

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