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A236383
Smallest k such that k^2 is a concatenation of two numbers x and y where y = x + n^2 and x and y have the same number of digits.
2
428, 453, 465, 381, 369, 358, 917, 421, 394, 452, 704, 716, 442, 833, 323, 380, 347, 697, 8376, 449, 3994, 407, 439, 431, 4770, 6961, 391, 336, 3533, 4277, 7915, 36332, 7705, 4487, 3323, 8869, 8942, 3250, 4560, 7632, 90951, 7988, 4204, 3606, 8586, 72774
OFFSET
1,1
COMMENTS
Conjecture: a(n) exists for all numbers n.
a(1) = A030467(1).
The same problem with the concatenation of x + n instead of x + n^2 is difficult.
The corresponding sequence with x + n instead of x + n^2 starts with 36363636364, 428, 8874, 5, 310, 7, 39 for n = 0,...,6, and a(7) > 10^70, if it exists. - Giovanni Resta, Jun 24 2019
LINKS
EXAMPLE
a(11) = 704 because 704^2 = 495616 is the concatenation of 495 and 616, and 616 - 495 = 121 = 11^2.
MAPLE
for n from 1 to 47 do:
ii:=0:
for k from 1 to 10^7 while(ii=0)do :
x:=convert(k^2, base, 10):n1:=nops(x):
if irem(n1, 2)=0
then
s:=sum('x[i]*10^(i-1) ', 'i'=1..n1/2):
z:=convert(s, base, 10):
s1:=sum('x[j]*10^(j-n1/2-1) ', 'j'=n1/2+1..n1):
if s-s1 = n^2
then
ii:=1:printf(`%d, `, k):
else
fi:
fi:
od:
od:
CROSSREFS
Cf. A030467.
Sequence in context: A251147 A095811 A235217 * A224668 A343536 A030467
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jan 24 2014
EXTENSIONS
Definition corrected by Giovanni Resta, Jun 24 2019
STATUS
approved