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%I #7 May 21 2024 05:28:11
%S 1,2,22,32,80,137,179,272,320,352,600,653,859,936,991,1279,1280,1306,
%T 1601,1609,1632,1672,1982,2089,2152,2437,2560,2591,2693,2789,2897,
%U 3120,3202,3701,3823,3847,4110,4212,4451,4691,4751,4919,5120,5182,5280,5386,5431,5479
%N Numbers k that divide the k-th tetranacci number (A000078).
%C Numbers k such that k | A000078(k).
%H Amiram Eldar, <a href="/A373054/b373054.txt">Table of n, a(n) for n = 1..10000</a>
%e 22 is a term since A000078(22) = 147312 = 22 * 6696 is divisible by 22.
%t With[{m = 10000}, Position[LinearRecurrence[{1, 1, 1, 1}, {0, 0, 1, 1}, m]/Range[m], _?IntegerQ] // Flatten]
%o (PARI) lista(kmax) = {my(t0 = 0, t1 = 0, t2 = 0, t3 = 1, t4 = 0); print1(1, ", ", 2, ", "); for(k = 4, kmax, t4 = t0 + t1 + t2 + t3; if(!(t4%k), print1(k, ", ")); t0 = t1; t1 = t2; t2 = t3; t3 = t4);}
%Y Cf. A000078.
%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K nonn
%O 1,2
%A _Amiram Eldar_, May 20 2024
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