|
|
A362069
|
|
Numbers k such that k+digitsum(k^2) is a square.
|
|
0
|
|
|
0, 17, 62, 71, 117, 125, 197, 206, 296, 297, 305, 413, 414, 557, 558, 692, 702, 711, 863, 864, 872, 873, 1062, 1070, 1071, 1268, 1493, 1502, 1727, 1736, 1737, 1745, 1998, 2006, 2267, 2276, 2285, 2564, 2565, 2573, 2879, 2888, 2889, 3221, 3222
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Conjecture: there are infinitely many pairs of consecutive terms. Example: (296,297); (413,414); (863,864).
|
|
LINKS
|
|
|
EXAMPLE
|
k=17 is a term because k^2=289 and 17+2+8+9=36=6^2.
|
|
MATHEMATICA
|
Select[Range[0, 3300], IntegerQ[Sqrt[# + Plus @@ IntegerDigits[#^2]]] &] (* Amiram Eldar, May 18 2023 *)
|
|
PROG
|
(PARI) isok(k)=issquare(k+sumdigits(k^2))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|