A329150 Increasingly ordered list without repetition of numbers k that are obtained, when, for nonnegative integers n, each nonzero digit d is replaced with prime(d).

0, 2, 3, 5, 7, 11, 13, 17, 19, 20, 22, 23, 25, 27, 30, 32, 33, 35, 37, 50, 52, 53, 55, 57, 70, 72, 73, 75, 77, 110, 112, 113, 115, 117, 130, 132, 133, 135, 137, 170, 172, 173, 175, 177, 190, 192, 193, 195, 197, 200, 202, 203, 205, 207, 211, 213, 217, 219, 220

Offset: 1

Author

Bernard Schott, Jan 11 2020

Keywords

• nonn
• base

Comments

As A329147 is not increasing, not decreasing, not surjective, not injective, another possible name could be: Terms of A329147 in increasing order without repetition.

No term can have digits 4, 6 or 8; also, no term begins with 9, 10, 12, 15, 29, 39, 59 or 79.

First primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 53, ...

First squares are 0, 25, 225, 2025, 2500, 3025, 7225, ...

First palindromes are 0, 2, 3, 5, 7, 11, 22, 33, 55, 77, 202, 222, 232, ...

Examples

			Prime(1) = 2, prime(5) = 11, so A329147(15) = 211 and 211 is a term.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..5365

Crossrefs

Cf. A329147, A329149 (complement).

Programs

PARI

f(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0); \\ A329147
lista(nn) = my(list = List(), m); for (n=0, nn, m = f(n); if (m <= nn, listput(list, m));); Set(list); \\ Michel Marcus, Mar 26 2023