cp's OEIS Frontend

A343740 a(n) is the digit position of the first appearance of the last digit to appear in sqrt(n) (or -1 if n is a square).

%I A343740 #16 Aug 06 2021 05:53:31
%S A343740 -1,19,23,-1,37,39,45,36,-1,27,17,25,15,36,19,-1,20,36,25,37,28,13,27,
%T A343740 52,-1,39,17,38,27,26,17,23,24,37,19,-1,25,26,26,41,58,57,25,12,25,22,
%U A343740 24,19,-1,33,48,23,41,49,23,32,32,23,30,19,17,31,27,-1,24
%N A343740 a(n) is the digit position of the first appearance of the last digit to appear in sqrt(n) (or -1 if n is a square).
%C A343740 A343739(n) is the last digit to appear in the decimal expansion of sqrt(n) (or -1 if n is a square), so a(n) is the digit position of the first appearance of the digit A343739(n) in sqrt(n).
%C A343740 (The first digit of sqrt(n) is counted as digit position 1; the decimal point is disregarded.)
%F A343740 a(100^q*n) = a(n), q > 0. - _Bernard Schott_, Jul 29 2021
%e A343740 a(2)=19 because A343739(2)=8 and the first appearance of an 8 in sqrt(2) = 1.414213562373095048... is at the 19th digit;
%e A343740 a(24)=52 because A343739(24)=0 and the first appearance of a 0 in sqrt(24) = 4.898979485566356196394568149411782783931894961313340... is at the 52nd digit.
%t A343740 Table[If[IntegerQ@ Sqrt@ n, -1, Function[s, Max@ Array[FirstPosition[s, #][[1]] &, 10, 0]]@ RealDigits[Sqrt[n], 10, 120][[1]]], {n, 65}] (* _Michael De Vlieger_, Jul 06 2021 *)
%o A343740 (Python 3.8+)
%o A343740 from math import isqrt
%o A343740 def A343740(n):
%o A343740     i = isqrt(n)
%o A343740     if i**2 == n:
%o A343740         return -1
%o A343740     m, dset, pos = n, set(), 0
%o A343740     for d in (int(s) for s in str(i)):
%o A343740         dset.add(d)
%o A343740         pos += 1
%o A343740         if len(dset) == 10:
%o A343740             return pos
%o A343740     while len(dset) < 10:
%o A343740         m *= 100
%o A343740         d = isqrt(m) % 10
%o A343740         dset.add(d)
%o A343740         pos += 1
%o A343740     return pos # _Chai Wah Wu_, Jul 07 2021
%Y A343740 Cf. A023961, A343739, A343741, A343742.
%K A343740 sign,base
%O A343740 1,2
%A A343740 _Jon E. Schoenfield_, Jul 05 2021