A014777 Position of the start of the first occurrence of n after the decimal point in Pi = 3.14159265358979323846264338327950288...

32, 1, 6, 9, 2, 4, 7, 13, 11, 5, 49, 94, 148, 110, 1, 3, 40, 95, 424, 37, 53, 93, 135, 16, 292, 89, 6, 28, 33, 186, 64, 137, 15, 24, 86, 9, 285, 46, 17, 43, 70, 2, 92, 23, 59, 60, 19, 119, 87, 57, 31, 48, 172, 8, 191, 130, 210, 404, 10, 4, 127, 219, 20, 312, 22, 7, 117, 98, 605

Offset: 0

Author

Paul Simon (paulsimn(AT)microtec.net) and Simon Plouffe

Keywords

• nonn
• base

Comments

This is A037008(1), A037000(1), A037001(1), A037002(1), A037003(1), A037004(1), A037005(1), A036974(1), A037006(1), A037007(1) etc.

Examples

			In the decimal expansion of Pi, the string "0" is found at position 32 counting from the first digit after the decimal point. The string "1" is found at position 1, the string "2" at position 6, the string "3" at position 9, etc.
		

Links

• Ronald R. King and T. D. Noe, Table of n, a(n) for n = 0..9999
• Dave Andersen, The Pi-Search Page.
• Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020)
• Anders Hellström, Sage program, Feb 02 2017

Crossrefs

Cf. A000796, A078197, A103186 (another version).

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007.

Programs

Magma

k := 700; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-3 + Pi(R)))), IntegerToString(n)) : n in [0..68] ]; /* Klaus Brockhaus, Feb 15 2007 */

Mathematica

Table[-1 + SequencePosition[#, IntegerDigits@ n][[1, 1]], {n, 0, 68}] &@ First@ RealDigits@ N[Pi, 10^4] (* Michael De Vlieger, Aug 10 2016, Version 10.1 *)

PARI

M14777=Map(); A014777(n)={iferr(mapget(M14777, n), E, my(i=if(n>9, A014777(n\10), 1), d=if(n, digits(n), [0]), j); while(i++, j=#d; until(!j, d[j]==A000796(i+j--) || next(2)); break); mapput(M14777, n, i--); i)} \\ M. F. Hasler, Jun 21 2022

Python

from mpmath import mp
def A014777(n):
    if not (i := A014777.pos.get(n, 0)):
        d = str(n); s = 2 # starting position for search
        while (i := A014777.pi.find(d, s)) < 1:
            s = max(len(A014777.pi) - len(d), 2)
            with mp.workdps(s + 99 if s < 500 else s*6//5): # new precision
                A014777.pi = str(mp.pi - 5/mp.mpf(10)**mp.dps) # don't round
        i -= 1; A014777.pos[n] = i
    return i
A014777.pi = ''; A014777.pos = {} # M. F. Hasler, Jun 21 2022

Extensions

More terms from Klaus Brockhaus, Feb 15 2007