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A265108
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The number of n-digit numbers in A264847 (pluritriangular numbers).
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3
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0, 4, 8, 19, 50, 142, 408, 1186, 3498, 10401, 31139, 93728, 283377, 859939, 2617798, 7990517, 24447214, 74950315, 230198869, 708160711, 2181656006, 6729833482, 20784165689, 64257670873, 198857204708, 615951476925
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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In order to find a closed formula for A264847, this sequence could be useful to point out the terms in which the increment changes. For example, the increment is (a(i) + 3) from the 13th to the 31st, (a(i) + 4) from the 32nd to the 81st, etc.
Conjecture: lim_{n -> infinity} a(n)/a(n-1) = sqrt(10).
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LINKS
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EXAMPLE
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a(1) = 4 because in A264847 there are 4 numbers with 1 digit (0, 1, 3, 6).
a(2) = 8 because in A264847 there are 8 numbers with 2 digits (10, 16, 24, 34, 46, 60, 76, 94).
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MATHEMATICA
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a = {0}; Do[AppendTo[a, a[[n - 1]] + Length@ Flatten@ Map[IntegerDigits, a]], {n, 2, 2000}]; Prepend[Most@ Map[Last, Tally[{1}~Join~IntegerLength@ Rest@ a]], 0] (* Michael De Vlieger, Dec 02 2015 *)
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PROG
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(Python)
a, b, d = 0, 0, 0
for g in range(1, 18):
h = 10**g
while a < h:
b = b + g
a = a + b
d = d + 1
print d
d = 0
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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