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A109210 In the decimal expansion of Pi, position of first digit of subsequence with total sum = 100. 3
2, 16, 30, 31, 39, 42, 45, 48, 53, 54, 66, 67, 68, 69, 71, 74, 94, 100, 103, 110, 111, 116, 119, 124, 126, 128, 131, 139, 140, 142, 145, 147, 148, 150, 152, 157, 160, 161, 162, 165, 166, 172, 174, 176, 180, 183, 184, 186, 191, 199, 201, 208, 209, 213, 230, 235 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

Take decimal expansion of Pi, s= 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4,1. Starting with the first term 3 add terms consecutively until we get sum = 100 or larger. If sum = 100 then a(1)=3. It is impossible to get 100 this way. Then we try starting with second digit, 1. It happens that the subsequence from i=2 to 21: s1={1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6} has a sum = 100, hence a(1)=2. Next similar subsequence with sum = 100 has i=16-37: s2={3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4}, hence a(2)=16, etc.

FORMULA

A109210(n)=A109212(n)-A109211(n)+1.

CROSSREFS

Position of the final digit in the subsequence gives A109211 and length of susequence gives A109212.

Sequence in context: A108705 A113933 A127871 * A056707 A069256 A120069

Adjacent sequences:  A109207 A109208 A109209 * A109211 A109212 A109213

KEYWORD

base,nonn

AUTHOR

Zak Seidov (zakseidov(AT)yahoo.com), Jun 22 2005

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Last modified February 17 21:13 EST 2012. Contains 206085 sequences.