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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..55.

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 *)

PROG

(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())))

(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

CROSSREFS

Cf. A337536.

Sequence in context: A207827 A047236 A039581 * A182218 A093701 A045601

Adjacent sequences:  A338417 A338418 A338419 * A338421 A338422 A338423

KEYWORD

nonn,base

AUTHOR

Devansh Singh, Oct 25 2020

STATUS

approved

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Last modified May 16 01:55 EDT 2021. Contains 343937 sequences. (Running on oeis4.)