A257279 - OEIS

%I #14 May 02 2015 07:56:32

%S 4,8,16,27,32,64,81,128,243,256,512,729,2187,3125,6561,8192,15625,

%T 16384,19683,32768,65536,78125,177147,262144,524288,531441,823543,

%U 1594323,1953125,4782969,9765625,16777216,33554432,48828125,134217728,268435456,282475249,1162261467

%N Zeroless prime powers p^m with p <= m.

%C A few years ago, challenges had been launched to find a prime power p^n, n>1 as large as possible, cf. links. I have remarked that it is easy to find arbitrarily large examples by taking the square of very large primes, rather than high powers of smaller primes, and suggested a merit function to take into account and penalize such "trivial" solutions. This led to a new challenge including the condition n > p. This sequence lists such numbers with the last condition relaxed to n >= p, which is sufficient to make the search nontrivial but includes a few more terms, namely the zeroless powers p^p (A051674 intersect A052382).

%C Possibly is a(80) = 19^44 the largest term; there are no greater ones in the first 500000 terms of A257278. - _Reinhard Zumkeller_, May 01 2015

%H Reinhard Zumkeller, <a href="/A257279/b257279.txt">Table of n, a(n) for n = 1..80</a>

%H S. S. Gupta, <a href="http://www.shyamsundergupta.com/canyoufind.htm">Can you find?</a>, CYF n° 410 (Jan. 26, 2010) and CYF n° 412 (Nov. 13, 2012).

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_607.htm">Puzzle 607. A zeroless Prime power</a>, primepuzzles.net, 2011

%o (PARI) is(n)=vecmin(digits(n)) && isprimepower(n,&n)>=n

%o (PARI) L=List();lim=10;forprime(p=1,lim,for(n=p,lim*log(lim)\log(p),listput(L,p^n)));listsort(select(n->vecmin(digits(n)),L));

%o (Haskell)

%o a257279 n = a257279_list !! (n-1)

%o a257279_list = filter ((== 1) . a168046) a257278_list

%o -- _Reinhard Zumkeller_, May 01 2015

%Y Cf. A052382, A000961, A025475; A122494.

%Y Equals A257278 \ A011540 = intersection of A052382 and A257278.

%Y Subsequence of A025475 \ A011540 and of A195943, see also A168046.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Apr 28 2015