A227802 Positive numbers of the form a^b +- 1 where a is in the sequence and b>1.

1, 2, 3, 5, 7, 8, 9, 10, 15, 17, 24, 26, 28, 31, 33, 48, 50, 63, 65, 80, 82, 99, 101, 124, 126, 127, 129, 224, 226, 242, 244, 255, 257, 288, 290, 342, 344, 511, 513, 575, 577, 624, 626, 675, 677, 728, 730, 783, 785, 960, 962, 999, 1001, 1023, 1025, 1088, 1090

Offset: 1

Author

Alexander E. Koren, Jul 31 2013

Keywords

• nonn

Examples

			1 is the seed value of the sequence. 2 is in the sequence because 2 = 1^2 + 1 and 1 is in the sequence. 3 is in the sequence because 3 = 2^2 - 1 and 2 is in the sequence.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080262.

Programs

PARI

is(n)=if(n<4,1,my(t);(ispower(n-1,,&t)&&is(t)) || (ispower(n+1,,&t)&&is(t))) \\ Charles R Greathouse IV, Aug 08 2013

PARI

list(lim)=my(v=List([1,2]),i=1);while(i++<=#v, for(e=2,log(lim+2)\log(v[i]), listput(v,v[i]^e-1);listput(v,v[i]^e+1))); vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Aug 08 2013

Python

def func(i):
 a=[2]
 pows={2:2}
 for rep in range(i):
  for x in a[:]:
   if not x**pows[x]-1 in a:
    a.append(x**pows[x]-1)
    pows[x**pows[x]-1]=2
   if not x**pows[x]+1 in a:
    a.append(x**pows[x]+1)
    pows[x**pows[x]+1]=2
   pows[x]+=1
  a.sort()
 return a