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A254034 Numbers representable as both b^c + b + c and x*y + x + y, where b, c, x, y are integers bigger than 1.

%I A254034 #15 Dec 28 2020 16:08:45
%S A254034 8,14,32,39,44,71,74,92,134,137,158,184,212,242,251,264,266,274,308,
%T A254034 344,353,422,464,523,554,602,634,704,741,758,814,872,932,994,1013,
%U A254034 1033,1036,1058,1124,1262,1334,1484,1562,1642,1724,1743,1808,1894,1982,2072,2164,2197
%N A254034 Numbers representable as both b^c + b + c and x*y + x + y, where b, c, x, y are integers bigger than 1.
%H A254034 Robert Israel, <a href="/A254034/b254034.txt">Table of n, a(n) for n = 1..10000</a>
%e A254034 a(1) = 8 = 2^2 + 2 + 2 = 2*2 + 2 + 2.
%e A254034 a(2) = 14 = 3^2 + 3 + 2 = 4*2 + 4 + 2.
%e A254034 a(3) = 32 = 5^2 + 5 + 2 = 10*2 + 10 + 2.
%p A254034 N:= 10000: # to get all entries <= N
%p A254034 A1:= {seq(seq(b^c+b+c, c = 2 .. floor(log[b](N))), b = 2 .. floor(sqrt(N)))}:
%p A254034 filter2:= proc(x) local x1;
%p A254034    x1:= x+1;
%p A254034    x <= N and not isprime(x1) and not(x1::even and isprime(x1/2))
%p A254034 end proc:
%p A254034 sort(convert(select(filter2,A1),list)); # _Robert Israel_, Dec 28 2020
%t A254034 mx = 2200; t = Transpose@ Flatten[ Table[{x^y + x + y, x*y + x + y}, {x, 2, Floor@ Sqrt@ mx}, {y, 2, Floor[mx/x]}], 1]; Intersection[ t[[1]], t[[2]]] (* _Robert G. Wilson v_, Jan 23 2015 *)
%Y A254034 Cf. A253916, A253917.
%K A254034 nonn
%O A254034 1,1
%A A254034 _Alex Ratushnyak_, Jan 23 2015