A369331 Positive numbers whose decimal expansions are covered by that of prime numbers (without leading zeros).

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 111, 112, 113, 115, 117, 119, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 171

Offset: 1

Author

Rémy Sigrist, Jan 20 2024

Keywords

• nonn
• base
• easy

Comments

More formally: positive numbers with decimal expansion (d_1, ..., d_w) (where d_1 <> 0) such that for any i in 1..w, we have some j, k such that j <= i <= k and d_j <> 0 and (d_j, ..., d_k) corresponds to the decimal expansion of a prime number.

This sequence contains, among others, A000040, A046034 and A152242.

This sequence first differs from A152242 for n = 42: a(42) = 111 whereas A152242(42) = 112.

Examples

			The number 15195 belongs to the sequence for the following covering:
       151
         19
           5
       .....
       15195
		

Links

• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A000040, A046034, A152242.

Programs

PARI

is(n, base = 10) = { my (d = if (n, digits(n, base), [0]), ok = vector(#d), rem = #d); for (i = 1, #d, if (d[i], for (j = i, #d, if  (isprime( fromdigits( d[i..j], base)), for (k = i, j, if (ok[k]==0, ok[k]++; rem--; if (rem==0, return (1)))))))); return (0); }