A080597 Minimum number of initial terms from the decimal expansion of Pi (A000796) to include every combination of n digits as a substring.

33, 607, 8556, 99850, 1369565, 14118313, 166100507, 1816743913, 22445207407, 241641121049, 2512258603208, 27261146164638, 294420436740326

Offset

1,1

Links

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

Eric Weisstein's World of Mathematics, Constant Digit Scanning

Eric Weisstein's World of Mathematics, Pi Digits

Formula

a(n) = A036903(n) + 1. - Eric W. Weisstein, Sep 11 2013

a(n) = A333128(A032510(n)) when A032510(n) has n digits; M(10^n-1) <= a(n) <= M(1.1*10^n), where M(N) = max A333128({0, ..., N}). - M. F. Hasler, Jun 15 2026

Example

a(1) = 33 because the digit 0 appears first as the 33rd digit in the decimal expansion of Pi (where 3 is the first digit).
a(2) = 607 because the first 607 digits of Pi contain every conceivable 2-digit subsequence but the first 606 digits do not. The combination (6, 8) appears as 606th and 607th term in A000796.

Crossrefs

Cf. A000796 (decimal expansion of Pi).

Cf. A036903 (= a(n) - 1).

Cf. A032510 (last digit string when scanning the decimal expansion of Pi for all n-digit strings).

Cf. A333128 (position at which ends the first occurrence of n in digits of Pi).

Sequence in context: A197361 A282926 A172362 * A076684 A181382 A252926

Adjacent sequences: A080594 A080595 A080596 * A080598 A080599 A080600

Keyword

more,nonn,base

Author

Martin Hasch (martin(AT)mathematik.uni-ulm.de), Feb 23 2003

Extensions

a(7)-a(8) from Piotr Idzik, Nov 01 2011

a(9)-a(11) from A036903(n) + 1 by Eric W. Weisstein, Sep 11 2013

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

Definition improved by M. F. Hasler, Jun 15 2026

Status

approved