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

1,2

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

Links

Table of n, a(n) for n=1..52.

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

Example

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

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 *)

Crossrefs

Cf. A007583, A002061, A059055.

Sequence in context: A154831 A206944 A206943 * A197318 A109492 A176799

Adjacent sequences: A059051 A059052 A059053 * A059055 A059056 A059057

Keyword

nonn

Author

Henry Bottomley, Dec 21 2000

Status

approved