

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
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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 PiSearch link [Andersen], through which 100 million digits of Pi are currently available.  Rick L. Shepherd, Oct 10 2002
200 million digits now available at PiSearch page.  Rick L. Shepherd, Aug 06 2006


REFERENCES

Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, p. 32.


LINKS



FORMULA



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

Cf. A000796: Decimal expansion (or digits) of Pi.


KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS

Additional term a(9), using subidiom search engine, from M. F. Hasler, Apr 13 2019


STATUS

approved



