A253776 -id:A253776 - cp's OEIS frontend

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

Alex Ratushnyak, Jan 12 2015

nonn

			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

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

Cf. A253776, A253777.

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

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 *)

A253777 Numbers representable as x^y + x + y in two or more ways, where x>1, y>1 are integers.

Original entry on oeis.org

22, 523, 531456, 16777232, 281474976710684, 150094635296999160

Offset: 1

Alex Ratushnyak, Jan 12 2015

The sequence is infinite since it contains all the numbers (k^2)^(k^2-k)+k^2+k^2-k = k^(2k^2-2k)+k+2k^2-2k for k>1. - Giovanni Resta, May 19 2015

Let a, b, and k be integers such that m = ab(k^a-k^b)/(a-b) is an integer. Then, the number given by (x,y) = (k^a,m/a) is the same as that given by (k^b,m/b). The given terms correspond to (a,b,k) = (2,1,2), (3,1,2), (2,1,3), (3,2,2), (4,2,2)/(2,1,4), and (3,1,3). - Charlie Neder, Apr 19 2019

			a(1) = 22 = 2^4 + 2 + 4 = 4^2 + 4 + 2.
a(2) = 523 = 8^3 + 8 + 3 = 2^9 + 2 + 9.
a(3) = 531456 = 3^12 + 3 + 12 = 9^6 + 9 + 6.
a(4) = 16777232 = 4^12 + 4 + 12 = 8^8 + 8 + 8.
a(5) = 281474976710684 = 4^24 + 4 + 24 = 16^12 + 16 + 12.
a(6) = 150094635296999160 = 3^36 + 3 + 36 = 27^12 + 27 + 12.

Cf. A253775, A253776.

a(6) from Lars Blomberg, May 19 2015

A249444 Primes representable as p^q + p + q, where p and q are primes.

Original entry on oeis.org

13, 137, 251, 353, 2213, 4933, 24421, 78137, 148933, 205441, 371311, 493121, 524309, 571873, 912773, 1225153, 1594339, 4330913, 7189253, 13652161, 18191713, 21254213, 28629187, 31855333, 42508901, 49431233, 73560481, 81183173, 99253313, 178454113, 184220581, 192100613

Offset: 1

Alex Ratushnyak, Jan 12 2015

nonn

Cf. A053810, A065017, A066938, A096342, A253776.

cp's OEIS Frontend

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

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A253777 Numbers representable as x^y + x + y in two or more ways, where x>1, y>1 are integers.

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A249444 Primes representable as p^q + p + q, where p and q are primes.

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