A059054 Integers which can be written as (b^k+1)/(b+1) for positive integers b and k.

1, 3, 7, 11, 13, 21, 31, 43, 57, 61, 73, 91, 111, 133, 157, 171, 183, 205, 211, 241, 273, 307, 343, 381, 421, 463, 507, 521, 547, 553, 601, 651, 683, 703, 757, 813, 871, 931, 993, 1057, 1111, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893

Offset: 1

Author

Henry Bottomley, Dec 21 2000

Keywords

• nonn

Comments

It seems that all values are odd. For (b^k+1)/(b+1) to be an integer, it seems k must be odd. 2=(0^0+1)/(0+1) has been excluded since neither b nor k would be positive.

When k is a composite, a(n) is a composite.

These numbers are in the form of 111...1 (k of 1s) base b. - Lei Zhou, Feb 08 2012

Examples

			43 is in the sequence since (2^7+1)/(2+1)=129/3=43; indeed also (7^3+1)/(7+1)=344/8=43.
		

Links

• H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

Crossrefs

Cf. A007583, A002061, A059055.

Programs

Mathematica

max = 44; maxdata = (1 + max^3)/(1 + max); a = {}; Do[i = 1; While[i = i + 2; cc = (1 + m^i)/(1 + m); cc <= maxdata, a = Append[a, cc]], {m, 2, max}]; Union[a] (* Lei Zhou, Feb 08 2012 *)