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 A290977 First n-digit number to appear twice in a row in the decimal expansion of Pi. 2
 3, 59, 209, 9314, 64015, 886287, 7348278, 85105027 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS David G. Andersen, The Pi-Search Page. EXAMPLE 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)... 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 *) PROG (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 FrÃ¶hlich, 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 CROSSREFS Cf. A000796, A287994, A290984. Cf. A050279, A096755, A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763. Sequence in context: A155032 A107212 A002148 * A200957 A057175 A142642 Adjacent sequences:  A290974 A290975 A290976 * A290978 A290979 A290980 KEYWORD base,more,nonn AUTHOR Bobby Jacobs, Aug 16 2017 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 STATUS approved

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Last modified June 25 19:25 EDT 2022. Contains 354851 sequences. (Running on oeis4.)