A333658 a(n) is the greatest number m not yet in the sequence such that the primorial base expansions of n and of m have the same digits (up to order but with multiplicity).

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 14, 15, 12, 13, 10, 11, 16, 17, 18, 20, 19, 21, 22, 23, 24, 26, 25, 27, 28, 29, 30, 36, 32, 38, 66, 68, 31, 37, 33, 39, 67, 69, 62, 63, 44, 45, 74, 75, 96, 98, 97, 99, 104, 105, 126, 128, 127, 129, 134, 135, 60, 61, 42, 43, 72, 73

Offset

0,3

Comments

Leading 0's are ignored.

This sequence is a permutation of the nonnegative integers, which preserves the number of digits (A235224) and the sum of digits (A276150) in primorial base.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..30029

Rémy Sigrist, Scatterplot of the first 2*3*5*7*11*13*17 terms

Rémy Sigrist, PARI program for A333658

Index entries for sequences related to primorial base

Index entries for sequences that are permutations of the natural numbers

Formula

a(A002110(n)) = A002110(n) for any n >= 0.

Example

For n = 42:
- the primorial base representation of 42 is "1200",
- there are five numbers m with the same multiset of digits:
    m   prim(m)
    --  -------
    34  "1020"
    42  "1200"
    61  "2001"
    62  "2010"
    66  "2100"
- so a(34) = 66,
     a(42) = 62,
     a(61) = 61,
     a(62) = 42,
     a(66) = 34.

Prog

(PARI) See Links section.

Crossrefs

See A333659 and A337598 for similar sequences.

Cf. A002110, A235224, A276150.

Sequence in context: A358143 A078840 A358124 * A337598 A333221 A334438

Adjacent sequences: A333655 A333656 A333657 * A333659 A333660 A333661

Keyword

nonn,look,base

Author

Rémy Sigrist, Sep 02 2020

Status

approved