OFFSET
1,1
COMMENTS
This produces primes well above the base composite, like 22111 from 44.
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).
Primes in A123132. - Charles R Greathouse IV, May 28 2013
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
EXAMPLE
44 = 2^2 * 11^1 yields 22111, which is prime and so enters the sequence. Powers precede the prime factor.
MAPLE
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
MATHEMATICA
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 *)
Select[FromDigits[Flatten[IntegerDigits/@Reverse/@FactorInteger[#]]]&/@ Range[2, 300], PrimeQ] (* Harvey P. Dale, Nov 24 2017 *)
PROG
(PARI) list(maxx)={
n=3; cnt=0;
while(n<=maxx,
f=factorint(n); old=0;
\\ as we concatenate, code is f{digits of each p.f.&pwr}
for (i=1, #f[, 1],
new=(10^length( Str(f[i, 1]) ) *f[i, 2] + f[i, 1]);
q=new+(10^length(Str(new)) )*old; old=q );
if(isprime(q), print("entry from", n, " ", q);
cnt++); n++;
while(isprime(n), n++);
); }
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Bill McEachen, May 26 2013
STATUS
approved