A082591 Starting position of the first occurrence of n in the decimal expansion of Pi such that a(n) > a(n-1) for n >= 1.

32, 37, 53, 64, 70, 90, 98, 99, 101, 122, 163, 174, 220, 281, 295, 314, 396, 428, 446, 495, 600, 650, 661, 698, 803, 822, 841, 977, 1090, 1124, 1358, 1435, 1501, 1667, 1668, 1719, 1828, 1926, 1968, 1987, 2007, 2161, 2210, 2236, 2261, 2305, 2416, 2509, 2555

Offset

0,1

Comments

a(m)=c means that c + digit_length(m) - 1 is the minimal number of decimal digits of Pi after the decimal point containing all m+1 digit strings 0, 1, 2, ..., m in increasing order from left-to-right (with intervening digit strings of course) - but with some strings overlapping if m >= 34. a(10)=163 ==> 163+2-1=164 digits are necessary to contain in the 11 strings 0, 1, 2, ..., 10 in order.

Links

Table of n, a(n) for n=0..48.

Dave Andersen, Pi-Search Page

Eric Weisstein's World of Mathematics, Pi Digits.

Example

a(0) = 32, the position of the first 0 in the decimal expansion of Pi.
a(1) = 37, the position of the first 1 after the first 0.
a(33) = 1667, the starting position of the first string 33 such that
a(33) > a(32)=1501. a(34) = 1668, the starting position of the first string 34
such that a(34) > a(33)=1667. Note that these occurrences of 33 and 34 overlap.

Crossrefs

Cf. A014777 (position of first n).

Sequence in context: A258699 A188827 A030094 * A070624 A345491 A178099

Adjacent sequences: A082588 A082589 A082590 * A082592 A082593 A082594

Keyword

base,nonn

Author

Rick L. Shepherd, May 13 2003

Status

approved