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A380359 a(n) is the number of integers in base n such that all the integers given by their first k digits are divisible by k and which cannot be extended further.

%I A380359 #41 Feb 18 2025 08:59:49
%S A380359 1,3,8,21,54,145,367,1039,2492,6709,16799,46610,95597,368134,831886,
%T A380359 2245056,6084180,15798495,41456343,119786906,292818176,788255058,
%U A380359 2061079489,5753392327,14984432350
%N A380359 a(n) is the number of integers in base n such that all the integers given by their first k digits are divisible by k and which cannot be extended further.
%H A380359 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polydivisible_number">Polydivisible number</a>.
%e A380359 a(10)=2492 because from all A271374(10)=20457 polydivisible numbers, only 2492 cannot be further expanded into a larger polydivisible number. One such number is 4836545640368400: 4 is divisible by 1, 48 is divisible by 2, 483 is divisible by 3, 4836 is divisible by 4, and so on until 4836545640368400 which is divisible by 16; but one cannot extend it further since no digit (0 to 9) appended to 4836545640368400 would result in a number divisible by k=17.
%Y A380359 Cf. A271374, A109783, A109032.
%K A380359 nonn,base,more
%O A380359 2,2
%A A380359 _Inigo Quilez_, Jan 22 2025