A256516 Numbers obtained by removing the first a(n) > 0 decimal digits of Pi set new records for closeness to Pi.

1, 2, 102, 249, 294, 1635, 3647, 5105, 6954, 357593, 416507, 497533, 821581, 1299504, 1457054, 39082410, 45969853, 47607985, 86389357, 121338042, 183331620, 191525092, 198003319, 388055713, 427238910, 570434345, 678096433

Offset

1,2

Comments

Suppose you forget the first a(n) digits of Pi after the 3, but remember the rest - these values are the record-setting best approximations to Pi.

a(28) > 4.9*10^9. - Robert G. Wilson v, Apr 03 2015

Links

Table of n, a(n) for n=1..27.

Example

a(1) = 1, giving an approximation 3.4159...
a(2) = 2, because 3.1592... is closer to Pi than 3.4159...
a(3) = 102, because 3.14808... is closer to Pi than any value obtained by removing fewer than 102 of the first decimal digits of Pi.
a(27) = 678096433, because 3.141592653607137185825... is closer to Pi than any value obtained by removing fewer than 678096433 of the first decimal digits of Pi. - Robert G. Wilson v, Apr 04 2015

Mathematica

pi = N[Pi - 3, 1000000]; k = 1; d = Infinity; lst = {}; While[k < 990000, pi = 10 pi - IntegerPart[10 pi]; If[ Abs[Pi - 3 - pi] < d, d = Abs[Pi - 3 - pi]; AppendTo[lst, k]; Print[k]]; k++]; lst (* Robert G. Wilson v, Apr 01 2015 *)

Prog

(Python)
def a256516():
....best = 1
....yield 1
....i = 2
....while True:
........if i>=len(pi):
............return
........a = pi[i]
........valid = True
........o = 1
........while valid:
............pi_approx = int(pi[:o])
............a_approx = abs(int(pi[i:i+o])-pi_approx)
............b_approx = abs(int(pi[best:best+o])-pi_approx)
............if abs(b_approx-a_approx)>10:
................valid = False
............else:
................o+=1
........if a_approx<b_approx:
............best = i
............yield i
........i+=1

Crossrefs

Cf. Decimal expansion of Pi: A000796.

Sequence in context: A068160 A173640 A111012 * A157066 A202740 A283624

Adjacent sequences: A256513 A256514 A256515 * A256517 A256518 A256519

Keyword

nonn,base,more

Author

Christian Perfect, Apr 01 2015

Extensions

a(10)-a(13) from Robert G. Wilson v, Apr 01 2015

a(14)-a(19) from Robert G. Wilson v, Apr 02 2015

a(20)-a(27) from Robert G. Wilson v, Apr 03 2015

Status

approved