cp's OEIS Frontend

A079665 Triangular array read by rows: row s contains integers of the form (2^s+1)/(2^r+1) in order of increasing r <= s-1.

%I A079665 #12 Feb 18 2024 12:42:27
%S A079665 3,11,13,43,171,57,205,683,241,2731,3277,10923,3641,993,43691,52429,
%T A079665 4033,174763,61681,699051,233017,16257,838861,2796203,65281,11184811,
%U A079665 1016801,13421773,44739243,14913081,261633,15790321,178956971,214748365
%N A079665 Triangular array read by rows: row s contains integers of the form (2^s+1)/(2^r+1) in order of increasing r <= s-1.
%C A079665 Conjecture: (b^s+1)/(b^r+1) is an integer if and only if: 1) r<s/2, 2) if s==1 (mod 2) then r is divisor of s, 3) if s=k*2^t with gcd(k,2^t)=1 then r is 2^t*u with u dividing k
%e A079665 s=2: no terms
%e A079665 s=3: 3
%e A079665 s=4: no terms
%e A079665 s=5: 11
%e A079665 s=6: 13
%e A079665 s=7: 43
%e A079665 s=8: no terms
%e A079665 s=9: 171, 57
%e A079665 ...
%o A079665 (PARI) for(x=2,30, for(y=1,x-1,if(Mod(2^x+1,2^y+1),0,print1((2^x+1)\(2^y+1)","))))
%Y A079665 Cf. A079672, A079581, A079673, A370425.
%K A079665 nonn,tabf
%O A079665 1,1
%A A079665 Jose R. Brox (tautocrona(AT)terra.es), Jan 25 2003
%E A079665 Definition corrected by _Max Alekseyev_, Feb 18 2024