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

0,1

Comments

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

Example

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.

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 *)

Prog

(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 */
(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

Crossrefs

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

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

Sequence in context: A351809 A176341 A134203 * A303323 A301910 A302154

Adjacent sequences: A014774 A014775 A014776 * A014778 A014779 A014780

Keyword

nonn,base

Author

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

Extensions

More terms from Klaus Brockhaus, Feb 15 2007

Status

approved