

A117746


Numbers of the form k^2  k  1 whose digit sum is also a number of the form k^2  k  1.


1



1, 5, 29, 41, 131, 155, 209, 379, 461, 551, 649, 991, 1055, 1121, 1189, 1639, 1721, 1891, 2351, 2449, 2755, 3079, 3305, 3781, 4159, 4421, 4555, 5699, 5851, 6005, 6319, 6805, 7309, 7831, 8371, 9505, 10099, 10301, 10505, 12431, 12655, 13339, 14761
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OFFSET

1,2


LINKS



EXAMPLE

5699 is in the sequence because 5699 = 76^2  76  1, the sum of its digits is 5 + 6 + 9 + 9 = 29, and 29 can be written as 6^2  6  1.


MATHEMATICA

nset=Table[n^2n1, {n, 200}]; Rest[Select[nset, MemberQ[nset, Total[ IntegerDigits[ #]]]&]] (* Harvey P. Dale, Jan 22 2011 *)


PROG

(PARI)
upto(n) = {
my(res = List());
for(i = 2, sqrtint(n) + 1,
c = i^2  i  1;
if(issquare(4*sumdigits(c) + 5),
listput(res, c)
)
);
res


CROSSREFS



KEYWORD

nonn,base


AUTHOR

Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006


STATUS

approved



