A226095 - OEIS

%I #43 Nov 25 2017 21:47:59

%S 13,1213,17,23,2213,113,1217,1223,12113,131,137,12119,22111,3217,167,

%T 173,179,43,221317,12143,22123,197,1103,1109,4217,22129,17117,211,

%U 12161,32117,13147,1327,1151,32119,23117,15131,17123,1163,1213129,13159,1181,1217113

%N Primes formed by concatenation (exponent then prime) of prime factorizations of the positive integers.

%C This produces primes well above the base composite, like 22111 from 44.

%C Entries stemming strictly from composite prime factorizations will be unique and the sequence will very likely be infinite. Of course not every prime will be encountered, and duplication will be seen across composite and prime factorization treated jointly (an example being 18 and 223 both yielding the prime 1223).

%C Primes in A123132. - _Charles R Greathouse IV_, May 28 2013

%H T. D. Noe, <a href="/A226095/b226095.txt">Table of n, a(n) for n = 1..10000</a>

%e 44 = 2^2 * 11^1 yields 22111, which is prime and so enters the sequence.  Powers precede the prime factor.

%p select(isprime, [seq((l-> parse(cat(seq([i[2], i[1]][], i=l))))(sort(ifactors(n)[2], (x, y)-> x[1]<y[1] or x[1]=y[1] and x[2]<y[2])), n=1..300)])[];  # _Alois P. Heinz_, Nov 24 2017

%t t = {}; Do[s = FromDigits[Flatten[IntegerDigits /@ RotateLeft /@ FactorInteger[n]]]; If[PrimeQ[s], AppendTo[t, s]], {n, 2, 200}]; t (* _T. D. Noe_, May 28 2013 *)

%t Select[FromDigits[Flatten[IntegerDigits/@Reverse/@FactorInteger[#]]]&/@ Range[2, 300],PrimeQ] (* _Harvey P. Dale_, Nov 24 2017 *)

%o (PARI) list(maxx)={

%o n=3;cnt=0;

%o while(n<=maxx,

%o f=factorint(n); old=0;

%o \\ as we concatenate, code is f{digits of each p.f.&pwr}

%o for (i=1,#f[,1],

%o new=(10^length(  Str(f[i,1]) )  *f[i,2] + f[i,1]);

%o q=new+(10^length(Str(new))   )*old;  old=q  );

%o if(isprime(q),  print("entry from", n, "   ",  q);

%o cnt++);  n++;

%o while(isprime(n),n++);

%o ); }

%Y Cf. A105435 (primes which with a 1 prepended stay prime).

%K easy,nonn,base

%O 1,1

%A _Bill McEachen_, May 26 2013