A244853 Let d(1)d(2)... d(q) denote the decimal expansion of a prime number n > 9. The sequence lists the primes such that replacing each digit d(i) with d(i+1) copies for i = 1..q-1 and d(q) with d(1) copies produces a prime. Zeros are not allowed.

11, 17, 71, 113, 131, 151, 167, 181, 211, 227, 281, 431, 467, 521, 547, 617, 743, 829, 853, 883, 1163, 1193, 1733, 2131, 2137, 3121, 3181, 3413, 3457, 3727, 4441, 5351, 6143, 6151, 6473, 6779, 6823, 6977, 8263, 8293, 8423, 9787, 11273, 11321, 11369, 11483

Offset: 1

Author

Michel Lagneau, Jul 07 2014

Keywords

• nonn
• base

Examples

			6473 is in the sequence because 6473 becomes 66664444444777333333 which is also prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057628.

Programs

Maple

for n from 5 to 2500 do:
     p := ithprime(n): s :=0: j :=0:
     x := convert(p, base, 10): n1 := nops(x):
     q := mul(x[i], i=1..n1):
     if q<>0 then
         for m from n1 by -1 to 2 do:
            s := s*10^x[m-1]+add(x[m]*10^(i-1+j),i=1.. x[m-1]):
         od:
         s1 := add(x[1]*10^(i-1), i=1..x[n1]):
         z := s*10^x[n1]+s1:
         if isprime(z) then printf(`%d, `, p) fi:
     fi:
od:

Mathematica

deQ[n_]:=Module[{idn=IntegerDigits[n]},idn=Join[idn,{idn[[1]]}];FreeQ[ idn,0] && PrimeQ[FromDigits[Flatten[Table[#[[1]],{#[[2]]}]&/@ Partition[ idn,2,1]]]]]; Select[ Prime[Range[5,1500]],deQ] (* Harvey P. Dale, Mar 26 2016 *)

PARI

isok(n) = {if (isprime(n) && (d=digits(n)) && (#d>1) && vecmin(d), s = ""; for (id = 1, #d, if (id != #d, idk = d[id+1], idk = d[1]); for (k=1, idk, s = concat(s, d[id]));); isprime(eval(s)););} \\ Michel Marcus, Jul 09 2014