A153230 Numbers k such that the string k is found at position k^2 in the decimal digits of Pi.

1, 3, 22, 596, 43934, 78778, 249994

Offset: 1

Author

Gil Broussard, Dec 21 2008

Keywords

• nonn
• base
• more

Comments

a(5) > 10^4, if it exists. - Amiram Eldar, May 06 2024

From Michael S. Branicky, May 19 2025: (Start)

a(8) > 10^6.

Assuming uniformly random digits, the expected value is 0.9 terms per digit-length. (End)

Examples

			22 is in the sequence because 22 occurs at position 484 (22^2) after the decimal point in the digits of Pi.
		

Crossrefs

Cf. A000796, A057679, A057680, A109513, A109514.

Programs

Mathematica

With[{m = 10^3}, s = Rest@ RealDigits[Pi, 10, m^2][[1]]; q[n_] := s[[n^2 + Range[0, IntegerLength[n] - 1]]] == RealDigits[n][[1]]; Select[Range[m - 1], q]] (* Amiram Eldar, May 06 2024 *)

Extensions

a(5)-a(7) from Michael S. Branicky, May 18 2025