|
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 27, 22, 23, 24, 25, 26, 21, 28, 29, 30, 31, 32, 45, 34, 35, 36, 37, 38, 33, 40, 41, 42, 43, 44, 81, 46, 47, 48, 49, 50, 75, 52, 53, 54, 125, 56, 63, 58, 59, 60, 61, 62, 39, 64, 55, 66, 67, 68, 135, 70, 71, 72, 73, 74, 51, 76, 77, 78, 79, 80, 99, 82, 83, 84, 175, 86, 105
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) tells which number in square array A246278 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have even numbers as their topmost row and primes as their leftmost column, both sequences are among the fixed points of this permutation.
Equally: a(n) tells which number in array A246279 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.
|
|
LINKS
|
|
|
FORMULA
|
As a composition of other permutations:
a(1) = 1, and for n > 1, a(n) = 1 + A249816(n-1).
Other identities. For all n >= 1:
|
|
MATHEMATICA
|
lim = 87; a003961[p_?PrimeQ] := a003961[p] = Prime[PrimePi@ p + 1]; a003961[1] = 1; a003961[n_] := a003961[n] = Times @@ (a003961[First@ #]^Last@ # &) /@ FactorInteger@ n; a055396[n_] := PrimePi[FactorInteger[n][[1, 1]]]; a078898 = Block[{nn = 90, spfs}, spfs = Table[FactorInteger[n][[1, 1]], {n, nn}]; Table[Count[Take[spfs, i], spfs[[i]]], {i, nn}]]; a246278 = NestList[Map[a003961, #] &, Table[2 k, {k, lim}], lim]; Table[a246278[[a055396@ n, a078898[[n]]]], {n, 2, lim}]
|
|
PROG
|
;; Alternatively:
|
|
CROSSREFS
|
Other similar or related permutations: A249816.
Cf. A000040, A005843, A020639, A055396, A078898, A083140, A083221, A246277, A246278, A246279, A249822.
Differs from its inverse A249817 for the first time at n=33, where a(33) = 45, while A249817(33) = 39.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|