A105435 -id:A105435 - cp's OEIS frontend

A023237 Primes p such that 10*p + 1 is also prime.

3, 7, 13, 19, 31, 43, 97, 103, 109, 151, 157, 181, 193, 211, 241, 271, 337, 349, 367, 409, 421, 439, 487, 523, 547, 571, 601, 613, 631, 691, 733, 769, 811, 823, 829, 883, 937, 1009, 1021, 1033, 1039, 1063, 1069, 1117, 1201, 1249, 1279, 1291, 1459, 1483, 1489

Offset: 1

David W. Wilson

Primes which with a 1 appended stay prime.
Corresponding values of 10n + 1 in A055781. - Jaroslav Krizek, Jul 14 2010
Subsequence of A024912. - Michel Marcus, May 21 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A024912, A055781, A105435, A005384 (2*p + 1), A158017 (10*p - 1).

[n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+1)]; // Vincenzo Librandi, Nov 20 2010

[p: p in PrimesUpTo(1100)| IsPrime(10*p+1)]; // Vincenzo Librandi, May 21 2014

with(numtheory); for i from 1 to 500 do if isprime(10*ithprime(i)+1) then printf(`%d,`, ithprime(i)) fi: od: # James Sellers, Apr 09 2005

Select[Prime[Range[ 240]], PrimeQ[FromDigits[Join[IntegerDigits[ # ], {1}]]] &] (* Robert G. Wilson v, Apr 09 2005 *)
Select[Prime[Range[900]], PrimeQ[10 # + 1] &] (* Vincenzo Librandi, May 21 2014 *)

Edited by N. J. A. Sloane at the suggestion of M. F. Hasler, Aug 24 2007

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

Original entry on oeis.org

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

Offset: 1

Bill McEachen, May 26 2013

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

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

T. D. Noe, Table of n, a(n) for n = 1..10000

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

select(isprime, [seq((l-> parse(cat(seq([i[2], i[1]][], i=l))))(sort(ifactors(n)[2], (x, y)-> x[1]Alois P. Heinz, Nov 24 2017

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 *)

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++);
); }

cp's OEIS Frontend

A023237 Primes p such that 10*p + 1 is also prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Magma

Maple

Mathematica

Extensions