A369331 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..60.

Index entries for sequences related to decimal expansion of n

EXAMPLE

The number 15195 belongs to the sequence for the following covering:

151

.....

15195

PROG

(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); }

CROSSREFS

Cf. A000040, A046034, A152242.

Sequence in context: A318719 A106317 A246281 * A152242 A166504 A095405

Adjacent sequences: A369328 A369329 A369330 * A369332 A369333 A369334

KEYWORD

nonn,base,easy

AUTHOR

Rémy Sigrist, Jan 20 2024

STATUS

approved