A082591 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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).