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%I #17 Feb 27 2020 22:30:01
%S 11,17,71,113,131,151,167,181,211,227,281,431,467,521,547,617,743,829,
%T 853,883,1163,1193,1733,2131,2137,3121,3181,3413,3457,3727,4441,5351,
%U 6143,6151,6473,6779,6823,6977,8263,8293,8423,9787,11273,11321,11369,11483
%N 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.
%H Harvey P. Dale, <a href="/A244853/b244853.txt">Table of n, a(n) for n = 1..1000</a>
%e 6473 is in the sequence because 6473 becomes 66664444444777333333 which is also prime.
%p for n from 5 to 2500 do:
%p p := ithprime(n): s :=0: j :=0:
%p x := convert(p, base, 10): n1 := nops(x):
%p q := mul(x[i], i=1..n1):
%p if q<>0 then
%p for m from n1 by -1 to 2 do:
%p s := s*10^x[m-1]+add(x[m]*10^(i-1+j),i=1.. x[m-1]):
%p od:
%p s1 := add(x[1]*10^(i-1), i=1..x[n1]):
%p z := s*10^x[n1]+s1:
%p if isprime(z) then printf(`%d, `, p) fi:
%p fi:
%p od:
%t 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 *)
%o (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
%Y Cf. A057628.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jul 07 2014
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