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