A266368 The smallest prime formed by the concatenation of consecutive n-th powers beginning with "1," plus a trailing "1.".

11, 1231, 149161, 181, 1168125662512961, 1321, 1647294096156251, 11282187163847812527993682354320971524782969100000001948717135831808627485171, 125665616553639062516796161, 15121

Offset: 0

Author

Thomas S. Pedigo, Dec 28 2015

Keywords

• nonn
• base

Comments

a(10) has 437 and a(11) has 1810 decimal digits respectively. - Michael De Vlieger, Jan 05 2016

a(13) is a bit more manageable, with 65 decimal digits - 18192159432367108864122070312513060694016968890104075497558138881. a(14) and a(15) are even shorter, with 23 and 15 decimal digits, respectively - 11638447829692684354561 and 132768143489071. - Thomas S. Pedigo, Jan 06 2016

Examples

			a(6)=1647294096156251; 1=1^6; 64=2^6; 729=3^6; 4096=4^6; 15625=5^6; 1647294096156251 is prime.
		

Crossrefs

Cf. A019521, A019522.

Programs

Mathematica

f[k_, n_] := FromDigits@ Flatten@ Map[IntegerDigits, Append[Range[k + 1]^n, 1], 1]; Table[If[n == 0, k = 0, k = 1]; While[! PrimeQ@ f[k, n], k++]; f[k, n], {n, 0, 9}] (* Michael De Vlieger, Jan 05 2016 *)