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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) by d(1) copies produces a prime. Zeros are not allowed. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)