A096760 -id:A096760 - cp's OEIS frontend

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

3, 59, 209, 9314, 64015, 886287, 7348278, 85105027

Offset: 1

Bobby Jacobs, Aug 16 2017

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

			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)...

David G. Andersen, The Pi-Search Page.

Cf. A000796, A287994, A290984.

Cf. A050279, A096755, A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763.

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 *)

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

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

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

A329368 Partition the decimal expansion of Pi into non-overlapping strings of length 10: 3141592653, 5897932384,..; a(n) is the position of the strings where digits are different from each other.

Original entry on oeis.org

7, 548, 3113, 11665, 11728, 14305, 15762, 19177, 23288, 28259, 35603, 37613, 40595, 40740, 41477, 52108, 54085, 54367, 62272, 74856, 75082, 75178, 82919, 83591, 92284, 94936, 103849, 105419, 105832, 108875, 111962, 115152, 117919, 118976, 121112, 124121, 128505

Offset: 1

XU Pingya, Apr 27 2020

			a(1) = 7, because such a string first occur at the 7th string: 4592307816 (i.e., 61-70 digits of Pi).

David Blatner, The Joy of Pi, Walker and Co., NY, 1997; page 91.

Eric Weisstein's World of Mathematics, Pi Digits

Cf. A000796, A014976, A050278, A096760, A101815, A101816, A107115.

q[i_]:=q[i]=Take[RealDigits[Pi,10,10i][[1]],-10];
a={}; Do[If[Length@Union@q[i]==10, AppendTo[a,i]], {i,130000}]
a

cp's OEIS Frontend

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

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