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A335839 Integers whose sum of digits in base b is the same for every prime b up to 13.

%I A335839 #28 Jun 12 2021 19:17:11
%S A335839 0,1,2007986541,2834822783,31939595966,33952616126,42737313983,
%T A335839 44878987167,309231463167,318362221465,415332522143,881935644447,
%U A335839 1898245489647,2077690289610,2077690289611,2153926044391,3998461033469,4285034622330,4285034622331,4294899857375
%N A335839 Integers whose sum of digits in base b is the same for every prime b up to 13.
%C A335839 This is a subset of A212222 for bases 2, 3, 5, 7, 11, which is a subset of A135127 for bases 2, 3, 5, 7, which is a subset of A135121 for bases 2 ,3, 5, which is a subset of A037301 for bases 2, 3. The third term also occurs in A212223.
%H A335839 Thomas König, <a href="/A335839/b335839.txt">Table of n, a(n) for n = 1..19840</a>
%e A335839 31939595966 is 11101101111101111111000111010111110_2, 10001102220222120211202_3, 1010403014032331_5, 2210331041405_7, 12600084203_11 and 3020180615_13. In these bases, the sum of digits is 26, so 31939595966 is a term.
%o A335839 (Python)
%o A335839 def digsum(n,b):
%o A335839     s = 0
%o A335839     while n > 0:
%o A335839         n, d = n//b, n%b
%o A335839         s = s+d
%o A335839     return s
%o A335839 p = [2,3,5,7,11,13]
%o A335839 n, a = 0, 0
%o A335839 while n <= 20:
%o A335839     s2, i = digsum(a,2), 1
%o A335839     while i < len(p) and digsum(a,p[i]) == s2:
%o A335839         i = i+1
%o A335839     if i == len(p):
%o A335839         print(a, end = ", ")
%o A335839         n = n+1
%o A335839     a = a+1 # _A.H.M. Smeets_, May 16 2021
%Y A335839 Cf. A212223, A212222, A135127, A135121, A037301.
%K A335839 nonn,base
%O A335839 1,3
%A A335839 _Thomas König_, Sep 13 2020