A338420 Numbers k having exactly one base b which is not a divisor of k+1, and k contains the digit b-1 in base b.

2, 4, 7, 8, 10, 13, 15, 19, 23, 25, 26, 29, 31, 36, 38, 40, 51, 53, 55, 59, 63, 71, 80, 82, 84, 86, 87, 99, 101, 107, 109, 119, 127, 128, 129, 137, 143, 151, 152, 155, 161, 167, 169, 209, 215, 227, 256, 259, 260, 261, 265, 266, 267, 269, 271

Offset: 1

Author

Devansh Singh, Oct 25 2020

Keywords

• nonn
• base

Comments

All the terms of A337536 are in this sequence except A337536(2)=3.

There are only 30 terms which are even up to n=124705.

Crossrefs

Cf. A337536.

Programs

Mathematica

baseCount[n_] := Count[Complement[Range[n + 1], Divisors[n + 1]], ?(MemberQ[ IntegerDigits[n, #], # - 1] &)]; Select[Range[1000], baseCount[#] == 1 &] (* _Amiram Eldar, Oct 25 2020 *)

PARI

isok(k) = sum(b=2, k+1, ((k+1) % b) && #select(x->(x==b-1), digits(k, b))) == 1; \\ Michel Marcus, Oct 30 2020

Python

def A338420(N):
    return list(filter(isA338420,range(1,N+1)))
def isA338420(n):
    counter=0
    if n==2 or n==4:
        return True
    if n%2==0:
        counter=1
    for b in range(3,(n//2) +1):
        if (n+1)%b!=0:
            counter=main_base_check(int(n/b),b)+counter
    return counter==1
def main_base_check(m,b):
    while m!=0:
        if m%b == b-1:
            return 1
        m = m//b
    return 0
print(A338420(int(input())))