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A068987 a(n) is the first position in the digit sequence 3,1,4,1,5,9,.... of Pi where the pattern "1,2,...,n" occurs (where position of the initial 3 is 1). 14
2, 149, 1925, 13808, 49703, 2458886, 9470345, 186557267, 523551503, 191278379840, 4368196101672 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
1. We may never know if a(n) is defined for all n.
2. We split up the digits of any number > 9 in the pattern, e.g., if n = 11, we search for the pattern "1,2,3,4,5,6,7,8,9,1,0,1,1".
3. The pattern "1,2,3,4,5,6" does not occur before the 100,000th term in the digit sequence of Pi.
Two more terms a(6) and a(7) were found via the referenced Pi-Search link [Andersen], through which 100 million digits of Pi are currently available. - Rick L. Shepherd, Oct 10 2002
200 million digits now available at Pi-Search page. - Rick L. Shepherd, Aug 06 2006
This sequence uses position = 1 for the initial digit 3 of Pi, while A121280(n) = a(n)-1 starts counting at 0, as does the "Pi search page" and sequences A035117, A050279 - A050287, A048940, A096755 - A096763. - M. F. Hasler, Mar 18 2017
a(10) > 2*10^9. - M. F. Hasler, Apr 13 2019
a(12) > 22*10^12. - Dmitry Petukhov, Jan 29 2020
REFERENCES
Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 32.
LINKS
D. G. Andersen, The Pi-Search Page
SubIdiom.com, Irrational numbers search engine: π = 3.14159.... (Search within 2*10^9 digits, since at least 2009, maybe 2002.)
FORMULA
a(n) = A121280(n) + 1. - M. F. Hasler, Apr 13 2019
MATHEMATICA
p = ToString[N[Pi, 50000]/10]; t = {1, 12, 123, 1234, 12345}; g[n_] := StringPosition[p, ToString[n]][[1]][[1]] - 2; Table[g[t[[i]]], {i, 1, 5}]
CROSSREFS
First occurrence of n times the same digit: A035117 (n '1's), A050281 (n '2's), A050282, A050283, A050284, A050286, A050287, A048940 (n '9's).
First occurrence of exactly n times the same digit: A096755 (exactly n '1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 (exactly n '9's), A050279 (exactly n '0's).
First occurrence of n: A176341; of concatenate(1,...,n): A121280 = A068987 - 1.
Cf. A000796: Decimal expansion (or digits) of Pi.
Sequence in context: A175974 A062596 A142415 * A273047 A209077 A141139
KEYWORD
nonn,base,more
AUTHOR
Joseph L. Pe, Apr 01 2002
EXTENSIONS
More terms from Rick L. Shepherd, Oct 10 2002
a(8) from Rick L. Shepherd, Aug 06 2006
Additional term a(9), using subidiom search engine, from M. F. Hasler, Apr 13 2019
a(10)-a(11) from Dmitry Petukhov, Jan 16 2020
STATUS
approved

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Last modified May 22 02:24 EDT 2024. Contains 372741 sequences. (Running on oeis4.)