cp's OEIS Frontend

A309101 Primes whose decimal representation can be written as a sequence of primes separated by single zeros.

%I A309101 #27 Jul 05 2022 12:42:40
%S A309101 307,503,1103,1303,1307,1907,2011,2017,2029,2053,2083,2089,2903,3011,
%T A309101 3019,3023,3037,3041,3061,3067,3079,3083,3089,4703,5011,5023,5059,
%U A309101 5303,5903,6703,7013,7019,7043,7079,7103,7307,7907,10103,10303,10903,11047,11059,11071,11083
%N A309101 Primes whose decimal representation can be written as a sequence of primes separated by single zeros.
%C A309101 In the Honaker-Caldwell link there is the example
%C A309101 2030507011013017019023029031037041043047053059061067071073079083089097
%C A309101 with 70 digits. It consists of the sequence of primes less than 100 separated by zeros.
%H A309101 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://primes.utm.edu/curios/page.php?number_id=129">Prime Curios!: 20305...89097 (70-digits)</a>
%e A309101 10103 is a term because 101 and 3 are primes separated by a single zero.
%t A309101 Take[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@(Riffle[#,0]&/@Tuples[Prime[ Range[ 30]],2]),PrimeQ]//Sort,50] (* _Harvey P. Dale_, Jul 05 2022 *)
%o A309101 (PARI) cut(d, b) = {my(nb = hammingweight(b), vs = vector(nb+1, k, ""), iz = 0, ind = 1); for (i=1, #d, if (d[i] == 0, iz ++; if (b[iz], ind++, vs[ind] = concat(vs[ind], d[i])), vs[ind] = concat(vs[ind], d[i]););); apply(x->eval(x), vs);}
%o A309101 isok(n) = {if (isprime(n), my(d = digits(n), dz = select(x->(x==0), d, 1), nbz = #dz); if (! nbz, return (0)); if (nbz > 1, for (k=2, #dz, if (dz[k] == dz[k-1] + 1, return (0)););); for (i=1, 2^nbz-1, my(b = binary(i)); while (#b < nbz, b = concat(0, b)); my(vstr = cut(d, b)); if (#select(x->isprime(x), vstr) == #vstr, return (1));););} \\ _Michel Marcus_, Aug 07 2019
%Y A309101 Cf. A000040.
%K A309101 nonn,base,nice
%O A309101 1,1
%A A309101 _Bernard Schott_, Jul 12 2019
%E A309101 Missing term 10903 and more terms from _Michel Marcus_, Aug 07 2019