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%I #24 Jan 05 2021 05:04:53
%S 1,3,39,331815,114126085737676800331815
%N a(1)=1; thereafter a(n+1) = a(n) + Product_{b=2..n+1} b^(1+floor(log_b(a(i)))).
%H Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1996__8_2_347_0">Automaticity IV: Sequences, sets, and diversity</a>, J. Théor. Nombres Bordeaux 8.2 (1996): 347-367. See Theorem 10 p. 353, but b<=i+2 is a typo.
%o (PARI) a(n) = if (n==1, 1, a(n-1) + prod(b=2, n, b^(1+logint(a(n-1), b)))); \\ _Michel Marcus_, Jan 04 2021
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 04 2018
%E Name corrected by _Michel Marcus_, Jan 04 2021
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