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A337109
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Sequence starting with a(1) = 2 and always extended with the product "n-th digit * n-th term". When the product is = 0, we don’t extend the sequence with 0 but with the smallest integer not yet present.
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1
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2, 4, 16, 16, 96, 96, 576, 5184, 31104, 279936, 1679616, 8398080, 58786560, 352719360, 1763596800, 1763596800, 14108774400, 56435097600, 169305292800, 169305292800, 169305292800, 1, 4, 8, 56, 504, 4536, 13608, 81648, 81648, 489888, 3429216, 30862944, 185177664, 185177664, 1111065984, 8888527872
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OFFSET
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1,1
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COMMENTS
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The biggest of the first 100 terms is a(40) = 1919922020352 (Kris Katterjohn).
If we take a record to be a term greater than or equal to the previous record, then records occur at:
a(1)-a(21)
a(39)-a(40)
a(170)-a(179)
a(231)-a(240)
a(720)-a(729)
a(2211)-a(2239)
a(7172)-a(7211)
a(16819)-a(16828)
a(28374)-a(28385)
a(350156)-a(350165)
a(1102329)-a(1102370)
a(1102370) = 2^165*3^87*5^10*7^15*72547
(End)
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LINKS
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EXAMPLE
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a(1) = 2, multiplied by the 1st digit of the sequence (2), is 4;
a(2) = 4, multiplied by the 2nd digit of the sequence (4), is 16;
a(3) = 16, multiplied by the 3rd digit of the sequence (1), is 16;
a(4) = 16, multiplied by the 4th digit of the sequence (6), is 96;
a(5) = 96, multiplied by the 5th digit of the sequence (1), is 96;
(...)
a(21) = 169305292800, multiplied by the 21st digit of the sequence (0), is 0; we don't extend the sequence with 0 but with the smallest unused integer yet, which is 1; thus a(22) = 1. Etc.
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MATHEMATICA
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FromDigits /@ Nest[Append[#1, If[#2 == 0, Block[{k = 1}, While[! FreeQ[FromDigits /@ #1, k], k++]; IntegerDigits[k]], IntegerDigits[#2]]] & @@ {#1, FromDigits[#1[[-1]] ]*Flatten[#1][[#2]]} & @@ {#, Length@ #} &, {{2}}, 36] (* Michael De Vlieger, Sep 16 2020 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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