A168168 Palindromic primes with d digits which have more than 3*d/2 distinct primes as substrings, for any d > 0.

373, 11311, 17971, 37273, 37573, 39293, 71317, 93739, 97379, 1193911, 1317131, 1371731, 1793971, 3166613, 3319133, 3337333, 3479743, 3716173, 3722273, 3763673, 3769673, 3774773, 3792973, 3793973, 3799973, 3916193, 7118117

Offset

1,1

Comments

The prime itself and its prime digits are counted among the prime substrings.

Links

Table of n, a(n) for n=1..27.

C. Caldwell, G.L. Honaker (Editors), Prime curios!: 13151715131, by M. F. Hasler, Nov. 2009.

Example

The prime 13151715131 is in the sequence since it is palindromic, of length 11, and contains the following 17 > 11*3/2 distinct primes as substrings: 3, 5, 7, 13, 17, 31, 71, 131, 151, 5171, 7151, 13151, 15131, 31517, 517151, 1315171513 and 13151715131.

Prog

(PARI) prime_substrings(p) = { p=Vec(Str(p)); select( x->isprime(x), vecsort( concat( vector( #p, i, vector( i, j, eval( concat( vecextract( p, Str(j".."i))))))), 8))} /* Note: In PARI version 2.4.2 (dvt CHANGES-1.1971), the syntax is select(L, f) instead of select(f, L). */
{forprime( p=2, default(primelimit), p==eval(concat(vecextract(Vec(Str(p)), "-1..1")))|next; #prime_substrings(p) > #Str(p)*3\2 & print1(p", "))}

Crossrefs

Sequence in context: A213300 A219444 A134161 * A226850 A208834 A171216

Adjacent sequences: A168165 A168166 A168167 * A168169 A168170 A168171

Keyword

base,nonn

Author

M. F. Hasler, Nov 23 2009

Status

approved