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

%I

%S 1,2,3,5,7,8,9,10,15,17,24,26,28,31,33,48,50,63,65,80,82,99,101,124,

%T 126,127,129,224,226,242,244,255,257,288,290,342,344,511,513,575,577,

%U 624,626,675,677,728,730,783,785,960,962,999,1001,1023,1025,1088,1090

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

%H Charles R Greathouse IV, <a href="/A227802/b227802.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%o (Python)

%o def func(i):

%o .a=[2]

%o .pows={2:2}

%o .for rep in range(i):

%o ..for x in a[:]:

%o ...if not x**pows[x]-1 in a:

%o ....a.append(x**pows[x]-1)

%o ....pows[x**pows[x]-1]=2

%o ...if not x**pows[x]+1 in a:

%o ....a.append(x**pows[x]+1)

%o ....pows[x**pows[x]+1]=2

%o ...pows[x]+=1

%o ..a.sort()

%o .return a

%o (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

%o (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

%Y Cf. A080262.

%K nonn

%O 1,2

%A _Alexander E. Koren_, Jul 31 2013

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Last modified May 8 05:46 EDT 2021. Contains 343653 sequences. (Running on oeis4.)