login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A108548 Fully multiplicative with a(prime(j)) = A108546(j), where A108546 is the lexicographically earliest permutation of primes such that after 2 the forms 4*k+1 and 4*k+3 alternate, and prime(j) is the j-th prime in A000040. 14
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14, 15, 16, 17, 18, 19, 20, 21, 26, 29, 24, 25, 22, 27, 28, 23, 30, 37, 32, 39, 34, 35, 36, 31, 38, 33, 40, 41, 42, 43, 52, 45, 58, 53, 48, 49, 50, 51, 44, 47, 54, 65, 56, 57, 46, 61, 60, 59, 74, 63, 64, 55, 78, 73, 68, 87, 70, 67, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative with a(2^e) = 2^e, else if p is the m-th prime then a(p^e) = q^e where q is the m/2-th prime of the form 4*k + 3 (A002145) for even m and a(p^e) = r^e where r is the (m-1)/2-th prime of the form 4*k + 1 (A002144) for odd m. - David A. Corneth, Apr 25 2022

Permutation of the natural numbers with fixed points A108549: a(A108549(n)) = A108549(n).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..26927

Index entries for sequences that are permutations of the natural numbers

MATHEMATICA

terms = 72;

A111745 = Module[{prs = Prime[Range[2 terms]], m3, m1, min},

     m3 = Select[prs, Mod[#, 4] == 3&];

     m1 = Select[prs, Mod[#, 4] == 1&];

     min = Min[Length[m1], Length[m3]];

     Riffle[Take[m3, min], Take[m1, min]]];

A108546[n_] := If[n == 1, 2, A111745[[n - 1]]];

A049084[n_] := PrimePi[n]*Boole[PrimeQ[n]];

a[n_] := If[n == 1, 1, Module[{p, e}, Product[{p, e} = pe; A108546[A049084[p]]^e, {pe, FactorInteger[n]}]]];

Array[a, terms] (* Jean-Fran├žois Alcover, Nov 19 2021, using Harvey P. Dale's code for A111745 *)

PROG

(PARI)

up_to = 26927; \\ One of the prime fixed points.

A108546list(up_to) = { my(v=vector(up_to), p, q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4, up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };

v108546 = A108546list(up_to);

A108546(n) = v108546[n];

A108548(n) = { my(f=factor(n)); f[, 1] = apply(A108546, apply(primepi, f[, 1])); factorback(f); }; \\ Antti Karttunen, Apr 25 2022

CROSSREFS

Cf. A002144, A002145, A049084, A108546, A108549 (fixed points), A332808 (inverse permutation).

Cf. also A332815, A332817 (this permutation applied to Doudna tree and its mirror image), also A332818, A332819.

Cf. also A267099, A332212 and A348746 for other similar mappings.

Sequence in context: A249157 A033621 A332808 * A333692 A333693 A322464

Adjacent sequences:  A108545 A108546 A108547 * A108549 A108550 A108551

KEYWORD

nonn,mult,look

AUTHOR

Reinhard Zumkeller, Jun 10 2005

EXTENSIONS

Name edited by Antti Karttunen, Apr 25 2022

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 17:17 EDT 2022. Contains 356945 sequences. (Running on oeis4.)