A272671 Numbers k such that the decimal number 1k is a square.
6, 21, 44, 69, 96, 156, 225, 296, 369, 444, 521, 600, 681, 764, 849, 936, 1025, 1236, 1449, 1664, 1881, 2100, 2321, 2544, 2769, 2996, 3225, 3456, 3689, 3924, 4161, 4400, 4641, 4884, 5129, 5376, 5625, 5876, 6129, 6384, 6641, 6900, 7161, 7424, 7689, 7956, 8225, 8496, 8769, 9044, 9321, 9600
Offset: 1
Examples
44 is a member because 144 = 12^2 is a square. 0 is not a member because 10 is not a square.
Links
- Davin Park, Table of n, a(n) for n = 1..20000
Programs
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Magma
[n: n in [1..10000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(1)))]; // Marius A. Burtea, Mar 21 2019
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Maple
t1:=[]; for k from 1 to 20000 do if issqr(k+10^length(k)) then t1:=[op(t1),k]; fi; od; t1;
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Mathematica
Flatten[n /. Solve[10^# + n == a^2 && 10^(# - 1) <= n < 10^# && a > 0, {n, a}, Integers] & /@ Range[3]] (* Davin Park, Feb 05 2017 *) Select[Range[10000],IntegerQ[Sqrt[10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Jul 20 2025 *) -
PARI
isok(n) = issquare(eval(concat(1, Str(n)))); \\ Michel Marcus, Mar 21 2019
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Python
from sympy.ntheory.primetest import is_square def ok(n): return is_square(int('1'+str(n))) print(list(filter(ok, range(9601)))) # Michael S. Branicky, Jun 21 2021
Extensions
Extended by Davin Park, Feb 05 2017