A071176 Smallest k such that the concatenation of n and k is a square (decimal notation).

6, 5, 6, 9, 29, 4, 29, 1, 61, 0, 56, 1, 69, 4, 21, 9, 64, 49, 6, 25, 16, 5, 104, 336, 6, 244, 225, 9, 16, 25, 36, 4, 64, 81, 344, 1, 21, 44, 69, 0, 209, 25, 56, 1, 369, 24, 61, 4, 284, 41, 84, 9, 29, 76, 225, 25, 6, 564, 29, 84, 504, 5, 504

Offset

1,1

Comments

a(n) = 1 correspond to n = A132356(m), m > 0. - Bill McEachen, Aug 31 2023

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

A000196(n . a(n)) = A071177(n) where "." stands for concatenation.

Example

a(5) = 29 as 529 = 23^2 and 5'i is nonsquare for i<29, A071177(5)=23.

Mathematica

nksq[n_]:=Module[{idn=IntegerDigits[n], k=0}, While[!IntegerQ[Sqrt[ FromDigits[Join[ idn, IntegerDigits[k]]]]], k++]; k]; Array[nksq, 70] (* Harvey P. Dale, Sep 28 2012 *)

Prog

(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a071176 n = fromJust $ findIndex (== 1) $
            map (a010052 . read . (show n ++) . show) [0..]
-- Reinhard Zumkeller, Aug 09 2011
(PARI) a(n)={if(issquare(10*n), 0, my(m=n, b=1); while(1, m*=10; my(r=(sqrtint(m+b-1)+1)^2-m); b*=10; if(r<b, return(r))))} \\ Andrew Howroyd, Jan 13 2023
(Python)
from math import isqrt
from sympy.ntheory.primetest import is_square
def A071176(n):
    m = 10*n
    if is_square(m): return 0
    a = 1
    while (k:=(isqrt(a*(m+1)-1)+1)**2-m*a)>=10*a:
        a *= 10
    return k # Chai Wah Wu, Feb 15 2023

Crossrefs

Cf. A000196, A071177, A245631, A132356.

Sequence in context: A126689 A243093 A101634 * A243091 A195786 A201330

Adjacent sequences: A071173 A071174 A071175 * A071177 A071178 A071179

Keyword

nonn,base,nice,look

Author

Reinhard Zumkeller, May 15 2002

Status

approved