来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a236694 Showing 1-1 of 1 %I A236694 %S A236694 21,55,377,17711,121393,5702887,19740274219868223167 %N A236694 Fibonacci numbers such that the difference between the greatest prime divisor and the smallest prime divisor equals twice a Fibonacci number. %C A236694 The corresponding indices of the Fibonacci numbers are 8, 10, 14, 22, 26, 34, 94. %C A236694 Property of this sequence: a(n) is a subset of A216893 where the sum of the prime divisors equals also twice a Fibonacci number. %C A236694 Each number of this sequence is semiprime p*q, q>p primes with p+q = f1 + f2 and q-p = f1-f2, where f1 and f2 are Fibonacci numbers => f1 = (p+q)/2 and f2=(q-p)/2. %e A236694 121393 = F(26) = 233*521 is in the sequence because 521 - 233 = 288 = 2*F(12), but also 233 + 521 = 2*377 = 2*F(14). %p A236694 with(numtheory):nn:=200:with(combinat,fibonacci):lst:={}:for i from 3 to nn do:lst:=lst union {fibonacci(i)}:od:for n from 1 to nn-3 do:f:=lst[n]: x:=factorset(f):n1:=nops(x): s:=x[n1]-x[1]:if {s/2} intersect lst = {s/2} then printf(`%d, `,f):else fi:od: %Y A236694 Cf. A008472, A000045, A216893. %K A236694 nonn,hard %O A236694 1,1 %A A236694 _Michel Lagneau_, Jan 30 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE