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A226095 Primes formed by concatenation (exponent then prime) of prime factorizations of the positive integers. 1
13, 1213, 17, 23, 2213, 113, 1217, 1223, 12113, 131, 137, 12119, 22111, 3217, 167, 173, 179, 43, 221317, 12143, 22123, 197, 1103, 1109, 4217, 22129, 17117, 211, 12161, 32117, 13147, 1327, 1151, 32119, 23117, 15131, 17123, 1163, 1213129, 13159, 1181, 1217113 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A128897 A201265 A221390 * A220619 A178560 A091781

Adjacent sequences:  A226092 A226093 A226094 * A226096 A226097 A226098

KEYWORD

easy,nonn,base

AUTHOR

Bill McEachen, May 26 2013

STATUS

approved

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Last modified May 26 04:43 EDT 2022. Contains 354074 sequences. (Running on oeis4.)