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A309101
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Primes whose decimal representation can be written as a sequence of primes separated by single zeros.
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3
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307, 503, 1103, 1303, 1307, 1907, 2011, 2017, 2029, 2053, 2083, 2089, 2903, 3011, 3019, 3023, 3037, 3041, 3061, 3067, 3079, 3083, 3089, 4703, 5011, 5023, 5059, 5303, 5903, 6703, 7013, 7019, 7043, 7079, 7103, 7307, 7907, 10103, 10303, 10903, 11047, 11059, 11071, 11083
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internal format)
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OFFSET
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1,1
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COMMENTS
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In the Honaker-Caldwell link there is the example
2030507011013017019023029031037041043047053059061067071073079083089097
with 70 digits. It consists of the sequence of primes less than 100 separated by zeros.
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LINKS
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EXAMPLE
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10103 is a term because 101 and 3 are primes separated by a single zero.
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MATHEMATICA
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Take[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@(Riffle[#, 0]&/@Tuples[Prime[ Range[ 30]], 2]), PrimeQ]//Sort, 50] (* Harvey P. Dale, Jul 05 2022 *)
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PROG
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(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); }
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
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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Missing term 10903 and more terms from Michel Marcus, Aug 07 2019
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STATUS
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approved
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