|
| |
|
|
A359973
|
|
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the concatenation of the decimal digits of n and a(n) or of a(n) and n yields a prime number.
|
|
1
|
|
|
|
1, 3, 2, 7, 9, 13, 4, 11, 5, 19, 8, 17, 6, 23, 31, 21, 12, 47, 10, 27, 16, 37, 14, 41, 39, 33, 20, 43, 32, 49, 15, 29, 26, 57, 59, 71, 22, 51, 25, 73, 24, 53, 28, 63, 61, 79, 18, 77, 30, 81, 38, 97, 42, 83, 69, 89, 34, 67, 35, 91, 45, 87, 44, 109, 99, 103, 58
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Leading zeros are ignored.
This sequence is a self-inverse permutation of the positive integers (for any positive number v, there are infinitely many prime numbers starting with 10*v+1, so infinitely many prime numbers that are the concatenation of v and some other positive integer).
There is only one fixed point: a(1) = 1.
|
|
|
LINKS
|
Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^10, showing primes in red, composite prime powers in gold, squarefree composites in dark green, and other numbers in blue, showing powerful numbers that are not prime powers in light blue.
|
|
|
EXAMPLE
|
The first terms, alongside the corresponding prime numbers, are:
n a(n) Corresponding prime numbers
-- ---- ---------------------------
1 1 {11}
2 3 {23}
3 2 {23}
4 7 {47}
5 9 {59}
6 13 {613}
7 4 {47}
8 11 {811}
9 5 {59}
10 19 {1019}
11 8 {811}
12 17 {1217}
|
|
|
MATHEMATICA
|
nn = 120; c[_] := False; a[1] = 1; c[1] = True; u = 2; Q[n_] := AnyTrue[{FromDigits[Join[d, #]], FromDigits[Join[#, d]]} & @@ {IntegerDigits[n], d}, PrimeQ]; Do[Set[{k, d}, {u, IntegerDigits[n]}]; While[Nand[! c[k], Q[k]], k++]; Set[{a[n], c[k]}, {k, True}]; If[k == u, While[c[u], u++]], {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, Jan 21 2023 *)
|
|
|
PROG
|
(PARI) See Links section.
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
