A267720 The smallest prime number formed by the concatenation of consecutive powers of n beginning with 1^0 = "1," and ending with a trailing "1" - or "0," if no such prime number exists.

0, 131, 1416641, 151, 16361, 17491, 181, 191, 0, 1111211, 11214417282073624883229859841, 0, 11419627441, 1151, 1162564096655361048576167772162684354564294967296687194767361099511627776175921860444161, 1171, 1181, 11936168591, 1201

Offset: 2

Author

Thomas S. Pedigo, Jan 19 2016

Keywords

• nonn
• base

Comments

It is not known whether solutions exist for A(2), A(10), or A(13); if there are any, they must be greater than 10^128.

A(10) has final exponent 35; "110100100010000...1000000000000000000000000000000000001", total length 667 digits. - Dana Jacobsen, Jan 22 2016

A(2) has exponent > 1100, length > 182841 digits. A(13) has exponent > 750, length > 314093 digits. - Dana Jacobsen, Jan 25 2016

Examples

			A(14)=11419627441; 14^0=1; 14^1=14; 14^2=196; 14^3=2744; 11419627441 is prime.
A(19)=11936168591; 19^0=1; 19^1=19; 19^2=361; 19^3=6859; 11936168591 is prime.
		

Crossrefs

Cf. A068704, A088622.

Programs

Mathematica

lim = 60; Table[SelectFirst[Rest@ FoldList[FromDigits@ Join[Most@ IntegerDigits@ #1, IntegerDigits[n^#2], {1}] &, 11, Range@ lim], PrimeQ], {n, 2, 20}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, Jan 25 2016, Version 10.2 *)

Extensions

a(8) corrected by Thomas S. Pedigo, Dec 08 2021