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

%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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Last modified June 18 12:25 EDT 2024. Contains 373481 sequences. (Running on oeis4.)