%I #9 Oct 23 2024 00:48:58
%S 1,2,3,4,231700599,1069467839,1156703470,1241186868,2533742848,
%T 2684864798,3037193808,5056780650,7073145000,7557047134,9623855878,
%U 12090760318,12120887700,13816479742,14430478270,15811947072,16864260048,20905152190,22735441078,23224253128,23269229774,23766221400,25175490262
%N Starts of runs of 3 consecutive integers that are terms in A377209.
%e 231700599 is a term since 231700599, 231700600 and 231700601 are all terms in A377209: 231700599/A007895(231700599) = 17823123 and 17823123/A007895(17823123) = 1980347 are integers, 231700600/A007895(231700600) = 23170060 and 23170060/A007895(23170060) = 2317006 are integers, and 231700601/A007895(231700601) = 21063691 and 21063691/A007895(21063691) = 1914881 are integers.
%o (PARI) zeck(n) = if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s); \\ _Charles R Greathouse IV_ at A007895
%o is1(k) = {my(z = zeck(k)); !(k % z) && !((k/z) % zeck(k/z)); }
%o lista(kmax) = {my(q1 = is1(1), q2 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}
%Y Cf. A007895, A376794 (binary analog).
%Y Subsequence of A328208, A328209, A328210, A377209 and A377271.
%K nonn,base,new
%O 1,2
%A _Amiram Eldar_, Oct 22 2024