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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 02:56 EDT 2021. Contains 345042 sequences. (Running on oeis4.)