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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: A197599 A197983 A351611 * 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 8 02:36 EDT 2024. Contains 375749 sequences. (Running on oeis4.)