A036903 Scan decimal expansion of Pi until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

32, 606, 8555, 99849, 1369564, 14118312, 166100506, 1816743912, 22445207406, 241641121048, 2512258603207, 27261146164637, 294420436740325

Offset

1,1

Comments

Technically A080597(n) = a(n)+1 better matches this definition. For example, the first digit '0' occurs only as the 33rd digit: The 33-digit number P(32) = floor(Pi*10^32) = 314159265358979323846264338327950 is the first of this kind to have a digit 0. So, when a(1) = 32 digits have been scanned, the 0 hasn't been seen yet. Similarly, the last two-digit string to occur is 68 == P(606) (mod 100): it is not seen until the 607 digits of P(606), i.e., the 607 initial digits of Pi, have been scanned. - M. F. Hasler, Jun 15 2026

Links

Table of n, a(n) for n=1..13.

Fabrice Bellard, Pi Digits

Eric Weisstein's World of Mathematics, Pi Digits

Formula

a(n) = A080597(n) - 1.

Crossrefs

Cf. A000796 (decimal expansion of Pi).

Cf. A080597 (= a(n) + 1).

Cf. A032445 (starting positions of the first occurrences of n the decimal expansion of Pi).

Cf. A032510 (last n-digit number seen when scanning for all n-digit numbers).

Cf. A036900-A036906.

Sequence in context: A022756 A332262 A088914 * A208828 A013699 A378296

Adjacent sequences: A036900 A036901 A036902 * A036904 A036905 A036906

Keyword

nonn,base,more,changed

Author

Michael Kleber

Extensions

a(8)-a(11) from fabrice(AT)bellard.org (Fabrice Bellard), Oct 23 2011

a(12)-a(13) from Michael Kleber, Apr 13 2026

Status

approved