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%I #7 Jul 09 2021 21:44:52
%S 0,1,70911040973874056146188543,77332999599545910254098143
%N Integers whose sum of digits in base b is the same for every prime b up to 17.
%C This is a subset of A335839 for bases 2,3,5,11,13, which 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.
%e 77332999599545910254098143 = 11111111110111111001100100111011111011111110101111110010001010111101111101011011011111_2 =
%e 1022220111022022121010102021222111100222120112011112120_3 = 10124120314223101043140143200022120033_5 = 3300561310042202241132326120022_7 = 7940063801000011830000282_11 = 1B101304100834600A304201_13 = 120802053643008116067_17. In these bases, the sum of digits is 63, so 77332999599545910254098143 is a term.
%Y Cf. A212223, A212222, A135127, A135121, A037301, A335839.
%K nonn,base,hard,more,less
%O 1,3
%A _Thomas König_, Jun 13 2021