A185366 First n-digit square in the digits of e.

1, 81, 676, 8281, 72900, 819025, 21609, 3644281, 59845696, 796707076, 2113884529, 736205184576, 1751509314916, 1751509314916, 5176216516900, 4737309139140769, 99398242392417424, 887828157705424896, 8576326547254681744, 2583667059970281481

Offset

1,2

Comments

Squares are allowed to have prefix 0 (see example).

a(18)-a(20) require 1.6, 2, 4.9 billion digits, respectively. - Michael S. Branicky, Dec 28 2022

Links

Table of n, a(n) for n=1..20.

Example

a(7) = 21609 is the first square that occurs in the sequence of the 7 decimal digits ...0021609...with the index 830 in A001113.

Maple

Digits := 10000: p0 := evalf(exp(1)):for d from 1 to 20 do: id:=0:for i from
  0 to 50000 while(id=0) do :q0:=trunc(p0*10^(i+d-1)): x:= irem(q0, 10^d): if sqrt(x)=floor(sqrt(x))  then printf(`%d, `, x):id:=1: else fi:od:od:

Prog

(Python)
from math import isqrt
from sympy import E, isprime
e = str(E.n(10**5))[2:] # or load from file using the pattern:
# with open('e.txt', 'r') as f: digits_of_e = f.readline()[2:]
def a(n): return next((t for k in range(len(e)-n) if isqrt(t:=int(e[k:k+n]))**2 == t), "more digits needed")
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Dec 28 2022

Crossrefs

Cf. A001113.

Sequence in context: A187433 A269055 A236876 * A232026 A133549 A235946

Adjacent sequences: A185363 A185364 A185365 * A185367 A185368 A185369

Keyword

nonn,base

Author

Michel Lagneau, Feb 20 2011

Extensions

a(11)-a(20) from Michael S. Branicky, Dec 28 2022

Status

approved