A341090 Fully multiplicative: for any prime p, if the reversal of p in base 10, say q, is prime, then a(p) = q, otherwise a(p) = p.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 14, 15, 16, 71, 18, 19, 20, 21, 22, 23, 24, 25, 62, 27, 28, 29, 30, 13, 32, 33, 142, 35, 36, 73, 38, 93, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 213, 124, 53, 54, 55, 56, 57, 58, 59, 60, 61, 26, 63, 64, 155, 66

Offset: 1

Author

Rémy Sigrist, Feb 13 2022

Keywords

• nonn
• base
• mult

Comments

This sequence is a self-inverse permutation of the natural numbers.

Examples

			For n = 377:
- 377 = 13 * 29,
- the reversal of 13, 31, is prime,
- the reversal of 29, 92, is not prime,
- so a(377) = 31 * 29 = 899.
		

Links

• Rémy Sigrist, Scatterplot of (n, a(n)) for n, a(n) <= 1000000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A004086, A071786, A235027.

Programs

Maple

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; mul((q->
     `if`(isprime(q), q, j[1]))(R(j[1]))^j[2], j=ifactors(n)[2])
    end:
seq(a(n), n=1..66);  # Alois P. Heinz, Feb 15 2022

Mathematica

f[p_, e_] := If[PrimeQ[(q = IntegerReverse[p])], q, p]^e; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 15 2022 *)

PARI

a(n) = { my (f=factor(n)); prod (k=1, #f~, my (p=f[k,1], e=f[k,2], q=fromdigits(Vecrev(digits(p)))); if (isprime(q), q, p)^e) }