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A014777 Position of the start of the first occurrence of n after the decimal point in Pi = 3.14159265358979323846264338327950288... 42
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 (list; graph; refs; listen; history; text; internal format)
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).
Sequence in context: A351809 A176341 A134203 * A303323 A301910 A302154
KEYWORD
nonn,base
AUTHOR
Paul Simon (paulsimn(AT)microtec.net) and Simon Plouffe
EXTENSIONS
More terms from Klaus Brockhaus, Feb 15 2007
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)