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A254313
Smallest number k such that no n-digit triangular number begins with k.
0
2, 8, 11, 60, 103, 532, 1002, 5100, 10002, 50316, 100002, 501000, 1000000, 5003162, 10000000, 50010000, 100000002, 500031623, 1000000002, 5000100000, 10000000000, 50000316228, 100000000002, 500001000000, 1000000000002, 5000003162278, 10000000000001
OFFSET
1,1
FORMULA
It appears that all even terms in the sequence are given by
a(2m) = (10^m)/2 + round(10^(m/2))
and all odd terms by
a(2m+1) = 10^m + floor(frac((sqrt(8*(100^m-1))-1)/2)/(1-sqrt(1/2))).
EXAMPLE
There exist 2-digit triangular numbers beginning with 1 (10, 15), 2 (21, 28), 3 (36), 4 (45), 5 (55), 6 (66), and 7 (78), but not 8, so a(2)=8.
There exist 5-digit triangular numbers beginning with every number from 1 through 99, and the first few 5-digit triangular numbers are 10011 (begins with 100), 10153 (begins with 101), 10296 (begins with 102), and 10440 (begins with 104), so a(5)=103.
CROSSREFS
Sequence in context: A146480 A093918 A332098 * A209429 A135132 A178060
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, May 03 2015
STATUS
approved