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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

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 *)

Crossrefs

Cf. A253916, A253917.

Sequence in context: A144842 A273843 A227867 * A225606 A117132 A064969

Adjacent sequences: A254031 A254032 A254033 * A254035 A254036 A254037

Keyword

nonn

Author

Alex Ratushnyak, Jan 23 2015

Status

approved