A253775 Numbers representable as x^y + x + y, where x>1, y>1 are integers (without multiplicity).

8, 13, 14, 22, 32, 33, 39, 44, 58, 71, 72, 74, 88, 92, 112, 133, 134, 137, 158, 184, 212, 225, 242, 251, 264, 266, 274, 308, 344, 353, 382, 422, 464, 508, 523, 554, 602, 634, 652, 704, 738, 741, 758, 814, 872, 932, 994, 1013, 1033, 1036, 1058, 1124, 1192, 1262, 1306

Offset

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..1000

Example

a(1) = 8 = 2^2 + 2 + 2.
a(2) = 13 = 2^3 + 2 + 3.
a(3) = 14 = 3^2 + 3 + 2.
a(4) = 22 = 2^4 + 2 + 4 = 4^2 + 4 + 2. - Wolfdieter Lang, Feb 03 2015

Maple

N:= 10000; # to get all terms <= N
select(`<=`, {seq(seq(x^y+x+y, y = 2..floor(log[x](N-x))),
      x=2..floor(sqrt(N)))}, N);
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Jan 14 2015

Mathematica

M = 2000;
Select[Table[x^y + x + y, {x, 2, Floor[Sqrt[M]]}, {y, 2, Floor[Log[x, M-x]] }] // Flatten, # <= M&] // Union (* Jean-François Alcover, Feb 27 2019, after Robert Israel *)

Crossrefs

Cf. A253776, A253777.

Sequence in context: A133192 A063684 A059194 * A168137 A252458 A271720

Adjacent sequences: A253772 A253773 A253774 * A253776 A253777 A253778

Keyword

nonn

Author

Alex Ratushnyak, Jan 12 2015

Status

approved