A242645 -id:A242645 - cp's OEIS frontend

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.

11, 421, 31, 41, 2551, 61, 71, 6481, 8191, 101

Offset: 1

Amarnath Murthy, Mar 04 2002

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

			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)

Cf. A242645 (for a(11)).

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

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]

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.

A242646 a(n) = concatenation of decimal expansions of powers of 11 (in increasing order).

Original entry on oeis.org

1, 111, 111121, 1111211331, 111121133114641, 111121133114641161051, 1111211331146411610511771561, 111121133114641161051177156119487171, 111121133114641161051177156119487171214358881, 1111211331146411610511771561194871712143588812357947691, 111121133114641161051177156119487171214358881235794769125937424601

Offset: 0

N. J. A. Sloane, May 23 2014

a(2) = 111121 is the first prime in this sequence (compare A242645).

There are no further primes through a(100). - Harvey P. Dale, Sep 12 2014

Alois P. Heinz, Table of n, a(n) for n = 0..42

Cf. A242645.

a:= proc(n) option remember;
      `if`(n=0, 1, parse(cat(a(n-1), 11^n)))
    end:
seq(a(n), n=0..10);  # Alois P. Heinz, May 24 2014

Module[{nn=15,c},c=IntegerDigits/@(11^Range[0,nn]);Table[FromDigits[ Flatten[ Take[c,n]]],{n,nn+1}]] (* Harvey P. Dale, Sep 12 2014 *)

a(n) is the concatenation of 1, 11, 121, 11^3, ... 11^(n-1), 11^n.

cp's OEIS Frontend

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.

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