A254034 Numbers representable as both b^c + b + c and x*y + x + y, where b, c, x, y are integers bigger than 1.
8, 14, 32, 39, 44, 71, 74, 92, 134, 137, 158, 184, 212, 242, 251, 264, 266, 274, 308, 344, 353, 422, 464, 523, 554, 602, 634, 704, 741, 758, 814, 872, 932, 994, 1013, 1033, 1036, 1058, 1124, 1262, 1334, 1484, 1562, 1642, 1724, 1743, 1808, 1894, 1982, 2072, 2164, 2197
Offset: 1
Keywords
Examples
a(1) = 8 = 2^2 + 2 + 2 = 2*2 + 2 + 2. a(2) = 14 = 3^2 + 3 + 2 = 4*2 + 4 + 2. a(3) = 32 = 5^2 + 5 + 2 = 10*2 + 10 + 2.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
N:= 10000: # to get all entries <= N A1:= {seq(seq(b^c+b+c, c = 2 .. floor(log[b](N))), b = 2 .. floor(sqrt(N)))}: filter2:= proc(x) local x1; x1:= x+1; x <= N and not isprime(x1) and not(x1::even and isprime(x1/2)) end proc: sort(convert(select(filter2,A1),list)); # Robert Israel, Dec 28 2020 -
Mathematica
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 *)
Comments