A081421 - OEIS

%I #3 Oct 01 2013 17:57:36

%S 1,17,353,8177,198593,4912337,122336033,3054149297,76315468673,

%T 1907542343057,47685459212513,1192108586037617,29802463602463553,

%U 745059330625296977,18626462930705797793,465661390253305305137

%N Quotient after one division by 2 of numbers of the form 3^(2n) + 5^(2n).

%C Except for the first term, these numbers always end in 3 and 7 and necessarily generate an odd number as the quotient upon a single division by 2. Indeed for even n, 3^n+5^n can be written as (4-1)^n + (4+1)^n = 4h+1 + 4i+1 for some h,i. Then we add and get 4(h+i)+2. Divide by 2 to get 2(h+i) + 1 and odd number.

%o (PARI) p3np5n(n) = { forstep(x=0,n,2, y = (3^x + 5^x)/2; print1(y" ") ) }

%K easy,nonn

%O 0,2

%A _Cino Hilliard_, Apr 20 2003