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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).
5

%I #48 Mar 29 2023 14:39:37

%S 0,2,3,5,7,11,13,17,19,20,22,23,25,27,30,32,33,35,37,50,52,53,55,57,

%T 70,72,73,75,77,110,112,113,115,117,130,132,133,135,137,170,172,173,

%U 175,177,190,192,193,195,197,200,202,203,205,207,211,213,217,219,220

%N 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).

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

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

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

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

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

%H Michel Marcus, <a href="/A329150/b329150.txt">Table of n, a(n) for n = 1..5365</a>

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

%o (PARI) f(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0); \\ A329147

%o 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

%Y Cf. A329147, A329149 (complement).

%K nonn,base

%O 1,2

%A _Bernard Schott_, Jan 11 2020