A104867 Records in A104865.

10, 22, 44, 49, 57, 70, 71, 82, 98, 100, 104, 119, 136, 139, 140, 149, 162, 163

Offset

1,1

Comments

Start with decimal expansion of Pi: s0=3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4,1,9,7,1,6,9,3,9,9,3,7,5,1,0,5,8,2,0,9,7,4,9,4,4,5,...

Divide s0 to the sections with the same final digits: s={3,1,4,1,5,9,2,6,5,3}, {5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5}, {0,2,8,8,4,1,9,7,1,6,9,3,9,9,3,7,5,1,0}, {5,8,2,0,9,7,4,9,4,4,5},...

Then A104865(n) = length of s(n): 10,22,19,11,...

A104866(n) = initial/final digits of s(n): 3,5,0,5,...

A104867 gives records in A104865.

Links

Table of n, a(n) for n=1..18.

Mathematica

pi = RealDigits[Pi, 10, 250000][[1]]; lst = {}; f := Block[{k = Position[pi, pi[[1]]][[2, 1]]}, pi = Drop[pi, k]; k]; Do[lst = {lst, f}, {n, 22500}]; lst = Flatten[lst]; lsu = {}; a = 0; Do[ If[lst[[n]] > a, a = lst[[n]]; AppendTo[lsu, a]], {n, 22500}]; lsu (* Robert G. Wilson v, Mar 29 2005 *)

Prog

(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(2*10**5))[:-1] # alternative to above
pi_digits = pi_digits.replace(".", "")
def afind():
    idx, record = 0, -1
    while idx < len(pi_digits):
        digit, idx, c = pi_digits[idx], idx+1, 2
        while idx < len(pi_digits) and pi_digits[idx] != digit:
            idx += 1; c += 1
        if c > record:
            record = c; print(c, end=", ")
        idx += 1
afind() # Michael S. Branicky, Oct 22 2021

Crossrefs

Cf. A000796, A104865, A104866, A104868, A104869, A104870, A104871.

Sequence in context: A063710 A157917 A242234 * A179877 A216048 A079861

Adjacent sequences: A104864 A104865 A104866 * A104868 A104869 A104870

Keyword

nonn,base,more

Author

Zak Seidov, Mar 29 2005

Extensions

a(7)-a(10) from Robert G. Wilson v, Mar 29 2005

a(11)-a(17) from Michael S. Branicky, Oct 22 2021

Status

approved