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A255535 Numbers representable as both b^c + b + c and x^y + x - y, where b, c, x, y are integers greater than 1. 1
14, 88, 65548, 33554459, 387420510, 1099511627800, 35184372088855, 3656158440063002 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

a(1) = 14 = 3^2 + 3 + 2 = 2^4 + 2 - 4.

a(2) = 88 = 3^4 + 3 + 4 = 9^2 + 9 - 2.

a(3) = 65548 = 4^8 + 4 + 8 = 16^4 + 16 - 4.

a(4) = 33554459 = 2^25 + 2 + 25 = 32^5 + 32 - 5.

a(5) = 387420510 = 3^18 + 3 + 18 = 27^6 + 27 - 6.

a(6) = 1099511627800 = 4^20 + 4 + 20 = 32^8 + 32 - 8.

a(7) = 35184372088855 = 8^15 + 8 + 15 = 32^9 + 32 - 9.

a(8) = 3656158440063002 = 6^20 + 6 + 20 = 36^10 + 36 - 10.

PROG

(Python)

TOP = 100000000

a = [0]*TOP

for y in range(2, TOP/2):

  if 2**y+2+y>=TOP: break

for x in range(2, TOP/2):

    k = x**y+x+y

    if k>=TOP: break

    a[k]=1

for y in range(2, TOP/2):

  if 2**y+2-y>=TOP: break

for x in range(2, TOP/2):

    k = x**y+x-y

    if k>=TOP: break

    if k>=0: a[k]|=2

print [n for n in range(TOP) if a[n]==3]

CROSSREFS

Cf. A254034.

Sequence in context: A116343 A259473 A202785 * A034544 A248060 A186257

Adjacent sequences:  A255532 A255533 A255534 * A255536 A255537 A255538

KEYWORD

nonn,more

AUTHOR

Alex Ratushnyak, Feb 24 2015

EXTENSIONS

a(5)-a(8) from Lars Blomberg, May 19 2015

STATUS

approved

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Last modified January 28 09:52 EST 2020. Contains 331319 sequences. (Running on oeis4.)