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A068704 a(n) = smallest prime obtained as the concatenation of n^k, n^(k-1), n^(k-2), ..., n^2, n, 1 for some k >= 1; or 0 if no such prime exists. 3
11, 421, 31, 41, 2551, 61, 71, 6481, 8191, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: a(n) > 0, that is, for every n there exists a k which yields a prime.

If we stop the search when the concatenation reaches 10^500 then the sequence would continue: ?, 207361728144121, 131, ?, 151, 655364096256161, 289171, 181, 191, ?, 211, ?, ?. - Sascha Kurz, Mar 27 2002

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

a(3) = 31 as the concatenation of 3^1 and 1 is prime, so here k = 1.

a(5) = 2551= concatenation of 5^2, 5 and 1 is prime, so here k = 2.

The known values are as follows:

n   k    a(n)

1   1    11

2   2    421

3   1    31

4   1    41

5   2    2551

6   1    61

7   1    71

8   2    6481

9   2    8191

10  1    101

11  ?    ? (see A242645)

12  4    207361728144121

13  1    131

14  ?    ?

15  1    151

16  4    655364096256161

17  2    289171

18  1    181

19  1    191

20  ?    ?

21  1    211

22  ?    ?

23  ?    ?

24  1    241

25  1    251

26  ?    ?

27  1    271

28  1    281

29  4    70728124389841291 (Jayanta Basu, May 21 2013)

30  6    7290000002430000081000027000900301 (Jayanta Basu, May 21 2013)

31  1    311

32  2    1024321

33  1    331

34  33   a(n) is an 877-digit number (Ray Chandler, Apr 06 2014)

35  6    1838265625525218751500625428751225351 (Jayanta Basu, May 21 2013)

MAPLE

for i from 1 to 23 do k := 0:

c := true:

while(c) do a := i^k:for j from k-1 to 0 by -1 do a := i^j+10^(floor(log(i^j)/log(10)+0.000001)+1)*a; end do:

k := k+1: if(a>10^500) then a := -k; break: end if:

if(isprime(a)) then c := false: end if: end do:

b[i] := a: end do: seq(b[k], k=1..23); # Warning: program may not compute a(n). - N. J. A. Sloane, May 22 2014

MATHEMATICA

Table[k=1; While[!PrimeQ[x=FromDigits[Flatten[IntegerDigits[Reverse[n^Range[0, k]]]]]] && k<30, k++]; If[k==30, x=0]; x, {n, 34}] (* Jayanta Basu, May 21 2013 *) [Warning: program may not compute a(n). - N. J. A. Sloane, May 22 2014]

CROSSREFS

Cf. A242645 (for a(11)).

Sequence in context: A285926 A197599 A197983 * A090558 A068135 A197770

Adjacent sequences:  A068701 A068702 A068703 * A068705 A068706 A068707

KEYWORD

base,hard,more,nonn

AUTHOR

Amarnath Murthy, Mar 04 2002

EXTENSIONS

Corrected by Lior Manor, May 07 2006

Entry revised by N. J. A. Sloane, May 22 2014 to reflect the fact that a(11) is presently unknown.

STATUS

approved

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)