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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.

%I A338420 #32 Dec 14 2020 23:56:04
%S A338420 2,4,7,8,10,13,15,19,23,25,26,29,31,36,38,40,51,53,55,59,63,71,80,82,
%T A338420 84,86,87,99,101,107,109,119,127,128,129,137,143,151,152,155,161,167,
%U A338420 169,209,215,227,256,259,260,261,265,266,267,269,271
%N 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.
%C A338420 All the terms of A337536 are in this sequence except A337536(2)=3.
%C A338420 There are only 30 terms which are even up to n=124705.
%t A338420 baseCount[n_] := Count[Complement[Range[n + 1], Divisors[n + 1]], _?(MemberQ[ IntegerDigits[n, #], # - 1] &)]; Select[Range[1000], baseCount[#] == 1 &] (* _Amiram Eldar_, Oct 25 2020 *)
%o A338420 (Python)
%o A338420 def A338420(N):
%o A338420     return list(filter(isA338420,range(1,N+1)))
%o A338420 def isA338420(n):
%o A338420     counter=0
%o A338420     if n==2 or n==4:
%o A338420         return True
%o A338420     if n%2==0:
%o A338420         counter=1
%o A338420     for b in range(3,(n//2) +1):
%o A338420         if (n+1)%b!=0:
%o A338420             counter=main_base_check(int(n/b),b)+counter
%o A338420     return counter==1
%o A338420 def main_base_check(m,b):
%o A338420     while m!=0:
%o A338420         if m%b == b-1:
%o A338420             return 1
%o A338420         m = m//b
%o A338420     return 0
%o A338420 print(A338420(int(input())))
%o A338420 (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
%Y A338420 Cf. A337536.
%K A338420 nonn,base
%O A338420 1,1
%A A338420 _Devansh Singh_, Oct 25 2020