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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A057628.

Sequence in context: A228031 A324795 A250716 * A102870 A136721 A107172

Adjacent sequences: A244850 A244851 A244852 * A244854 A244855 A244856

Keyword

nonn,base

Author

Michel Lagneau, Jul 07 2014

Status

approved