cp's OEIS Frontend

A226095 Primes formed by concatenation (exponent then prime) of prime factorizations of the positive integers.

%I A226095 #43 Nov 25 2017 21:47:59
%S A226095 13,1213,17,23,2213,113,1217,1223,12113,131,137,12119,22111,3217,167,
%T A226095 173,179,43,221317,12143,22123,197,1103,1109,4217,22129,17117,211,
%U A226095 12161,32117,13147,1327,1151,32119,23117,15131,17123,1163,1213129,13159,1181,1217113
%N A226095 Primes formed by concatenation (exponent then prime) of prime factorizations of the positive integers.
%C A226095 This produces primes well above the base composite, like 22111 from 44.
%C A226095 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 A226095 Primes in A123132. - _Charles R Greathouse IV_, May 28 2013
%H A226095 T. D. Noe, <a href="/A226095/b226095.txt">Table of n, a(n) for n = 1..10000</a>
%e A226095 44 = 2^2 * 11^1 yields 22111, which is prime and so enters the sequence.  Powers precede the prime factor.
%p A226095 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 A226095 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 A226095 Select[FromDigits[Flatten[IntegerDigits/@Reverse/@FactorInteger[#]]]&/@ Range[2, 300],PrimeQ] (* _Harvey P. Dale_, Nov 24 2017 *)
%o A226095 (PARI) list(maxx)={
%o A226095 n=3;cnt=0;
%o A226095 while(n<=maxx,
%o A226095 f=factorint(n); old=0;
%o A226095 \\ as we concatenate, code is f{digits of each p.f.&pwr}
%o A226095 for (i=1,#f[,1],
%o A226095 new=(10^length(  Str(f[i,1]) )  *f[i,2] + f[i,1]);
%o A226095 q=new+(10^length(Str(new))   )*old;  old=q  );
%o A226095 if(isprime(q),  print("entry from", n, "   ",  q);
%o A226095 cnt++);  n++;
%o A226095 while(isprime(n),n++);
%o A226095 ); }
%Y A226095 Cf. A105435 (primes which with a 1 prepended stay prime).
%K A226095 easy,nonn,base
%O A226095 1,1
%A A226095 _Bill McEachen_, May 26 2013