cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A288291 Position of the first time an n-digit number appears twice in a row after the decimal point of e.

Original entry on oeis.org

31, 49, 97, 2, 112869, 5005575, 1561314, 69682897, 1841794338
Offset: 1

Views

Author

Bobby Jacobs, Sep 01 2017

Keywords

Comments

18281828 appears in e before any 1-digit, 2-digit, or 3-digit number appears twice in a row.

Examples

			a(1) = 31 because the first time a 1-digit number appears twice in a row in the decimal expansion of e is 31 digits after the decimal point: 2.718281828459045235360287471352(66)...
		

Crossrefs

Programs

  • Mathematica
    s = First@ RealDigits[E, 10, 51*^5]; Table[p = Partition[s, k, 1];
    SelectFirst[ Range[ Length[p] - k], p[[#]] == p[[# + k]] &] - 1, {k, 7}] (* Giovanni Resta, Sep 05 2017 *)

Extensions

a(6)-a(8) from Giovanni Resta, Sep 05 2017
a(9) from Michael S. Branicky, Jan 20 2023

A290977 First n-digit number to appear twice in a row in the decimal expansion of Pi.

Original entry on oeis.org

3, 59, 209, 9314, 64015, 886287, 7348278, 85105027
Offset: 1

Views

Author

Bobby Jacobs, Aug 16 2017

Keywords

Comments

209209 and 305305 appear in Pi before any 2-digit number appears twice in a row.
a(n) (n >= 1) begins at the following decimal places: 24, 413, 326, 8239, 107472, 1632152, 9719518. - Robert G. Wilson v, Aug 23 2017

Examples

			a(1) = 3 because 3 is the first 1-digit number to appear twice in a row in the decimal expansion of Pi = 3.14159265358979323846264(33)...
		

Crossrefs

Programs

  • Mathematica
    With[{s = Rest@ First@ RealDigits[N[Pi, 10^4]]}, Keys@ Merge[#, Identity] &@ Table[If[Length@ # > 0, TakeSmallest[#, 1], 0 -> 0] &@ Sort[Map[#[[1, 1]] &, DeleteCases[#, {}]]] &@ Map[SequenceCases[#, {a_, b_} /; b == a + n] &, KeyMap[FromDigits, PositionIndex@ Partition[s, n, 1]]], {n, 4}]] (* Michael De Vlieger, Aug 16 2017 *)
    pi = StringDrop[ ToString[ N[Pi, 1632200]], 2]; f[n_] := Block[{k = 1}, While[ StringTake[pi, {k, k +n -1}] != StringTake[pi, {k +n, k +2n -1}], k++]; k]; Array[f, 6] (* Robert G. Wilson v, Aug 17 2017 *)
  • PARI
    eva(n) = subst(Pol(n), x, 10)
    pistring(n) = default(realprecision, n+10); my(x=Pi); floor(x*10^n)
    pidigit(n) = pistring(n)-10*pistring(n-1)
    consecpidigits(pos, len) = my(v=vector(len)); for(k=1, len, v[k]=pidigit(pos+k)); v
    a(n) = my(v=[], w=[], x=1); while(1, v=consecpidigits(x, n); w=consecpidigits(x+n, n); if(v==w, return(eva(v))); x++) \\ Felix Fröhlich, Aug 16 2017
    
  • Python
    from sympy import S
    # download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
    # with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()
    pi_digits = str(S.Pi.n(3*10**5+2))[:-2] # alternative to above
    pi_digits = pi_digits.replace(".", "")
    def a(n):
        for k in range(1, len(pi_digits)-n):
            s = pi_digits[k:k+2*n]
            if s[0] != 0 and s[:len(s)//2] == s[len(s)//2:]:
                return int(s[:len(s)//2])
    print([a(n) for n in range(1, 6)]) # Michael S. Branicky, Jan 10 2022

Extensions

a(6) from Robert G. Wilson v, Aug 19 2017
a(7) from Bobby Jacobs, Aug 22 2017
a(8) from Michael S. Branicky, Jan 10 2022
Showing 1-2 of 2 results.