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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
0, 131, 1416641, 151, 16361, 17491, 186451240963276826214420971521, 191, 0, 1111211, 11214417282073624883229859841, 0, 11419627441, 1151, 1162564096655361048576167772162684354564294967296687194767361099511627776175921860444161, 1171, 1181, 11936168591, 1201 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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

LINKS

Table of n, a(n) for n=2..20.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A068704, A088622.

Sequence in context: A224843 A033530 A222876 * A263299 A330202 A243832

Adjacent sequences:  A267717 A267718 A267719 * A267721 A267722 A267723

KEYWORD

nonn,base

AUTHOR

Thomas S. Pedigo, Jan 19 2016

STATUS

approved

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Last modified April 10 01:41 EDT 2020. Contains 333392 sequences. (Running on oeis4.)