A117746 Numbers of the form k^2 - k - 1 whose digit sum is also a number of the form k^2 - k - 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

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

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^2-n-1, {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
} \\ David A. Corneth, Jan 04 2024

Crossrefs

Cf. A028387.

Sequence in context: A167742 A107151 A340154 * A156053 A081116 A192090

Adjacent sequences: A117743 A117744 A117745 * A117747 A117748 A117749

Keyword

nonn,base

Author

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

Status

approved