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%I #20 Jan 04 2024 14:15:00
%S 1,5,29,41,131,155,209,379,461,551,649,991,1055,1121,1189,1639,1721,
%T 1891,2351,2449,2755,3079,3305,3781,4159,4421,4555,5699,5851,6005,
%U 6319,6805,7309,7831,8371,9505,10099,10301,10505,12431,12655,13339,14761
%N Numbers of the form k^2 - k - 1 whose digit sum is also a number of the form k^2 - k - 1.
%H David A. Corneth, <a href="/A117746/b117746.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t nset=Table[n^2-n-1,{n,200}];Rest[Select[nset,MemberQ[nset,Total[ IntegerDigits[ #]]]&]] (* _Harvey P. Dale_, Jan 22 2011 *)
%o (PARI)
%o upto(n) = {
%o my(res = List());
%o for(i = 2, sqrtint(n) + 1,
%o c = i^2 - i - 1;
%o if(issquare(4*sumdigits(c) + 5),
%o listput(res, c)
%o )
%o );
%o res
%o } \\ _David A. Corneth_, Jan 04 2024
%Y Cf. A028387.
%K nonn,base
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006
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