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A309101 Primes whose decimal representation can be written as a sequence of primes separated by single zeros. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..44.

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!: 20305...89097 (70-digits)

EXAMPLE

10103 is a term because 101 and 3 are primes separated by a single zero.

MATHEMATICA

Take[Select[FromDigits[Flatten[IntegerDigits/@#]]&/@(Riffle[#, 0]&/@Tuples[Prime[ Range[ 30]], 2]), PrimeQ]//Sort, 50] (* Harvey P. Dale, Jul 05 2022 *)

PROG

(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

CROSSREFS

Cf. A000040.

Sequence in context: A142376 A261289 A142255 * A098042 A125252 A308785

Adjacent sequences: A309098 A309099 A309100 * A309102 A309103 A309104

KEYWORD

nonn,base,nice

AUTHOR

Bernard Schott, Jul 12 2019

EXTENSIONS

Missing term 10903 and more terms from Michel Marcus, Aug 07 2019

STATUS

approved

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Last modified November 27 00:20 EST 2022. Contains 358362 sequences. (Running on oeis4.)