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A376048 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} = 3,1,4,1,5,... are the digits of Pi (cf. A000796).

%I A376048 #32 Oct 18 2024 18:51:43
%S A376048 4,5,81,1621,13130101,310319170452181,21399552788917656689963823241,
%T A376048 1373822578697020375503379392874191898311737749943783762521
%N A376048 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} = 3,1,4,1,5,... are the digits of Pi (cf. A000796).
%D A376048 Rémy Sigrist and N. J. A. Sloane, Dampening Down a Divergent Series, Manuscript in preparation, September 2024.
%H A376048 Alois P. Heinz, <a href="/A376048/b376048.txt">Table of n, a(n) for n = 1..12</a>
%F A376048 a(n+1) = b(n+1)*A376049(n) + 1.
%p A376048 For Maple code for all these sequences, see A376056.
%Y A376048 Cf. A000796, A375531, A375532.
%Y A376048 See also A374663, A375516, A375781, A375522, A376048-A376062.
%K A376048 nonn,base
%O A376048 1,1
%A A376048 _N. J. A. Sloane_, Sep 13 2024