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A048529 a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 0's.

%I A048529 #29 Feb 16 2025 08:32:40
%S A048529 0,24,100,624,1000,10001,10000,100001,100000,1000001,1000000,10000001,
%T A048529 10000000,100000001,100000000,1000000001,1000000000,10000000001,
%U A048529 10000000000
%N A048529 a(n) is the smallest value of m such that A002378(m), the m-th oblong number, contains exactly n 0's.
%H A048529 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PronicNumber.html">Pronic Number</a>
%e A048529 From _Jesse Sealand_, Oct 05 2019: (Start)
%e A048529 a(1) = 0 since A002378(0) = 0;
%e A048529 a(2) = 24 since A002378(24) = 600;
%e A048529 a(3) = 100 since A002378(100) = 10100;
%e A048529 a(4) = 624 since A002378(624) = 390000, etc.
%e A048529 (End).
%t A048529 a[n_] := Block[{a = 0}, While[Count[IntegerDigits[a*(a + 1)], 0] != n, ++a]; Return[a]]; a /@ Range[1, 10] (* _Julien Kluge_, Dec 15 2016 *)
%Y A048529 Cf. A002378, A048530.
%Y A048529 Cf. A048531, A048533, A048535, A048537, A048539, A048541, A048543, A048545, A048547.
%K A048529 nonn,base,more
%O A048529 1,2
%A A048529 _Patrick De Geest_, May 15 1999
%E A048529 a(16)-a(19) from _Lars Blomberg_, Jun 10 2011
%E A048529 Name edited by _Jesse Sealand_, Oct 05 2019