A049345 n written in primorial base.

0, 1, 10, 11, 20, 21, 100, 101, 110, 111, 120, 121, 200, 201, 210, 211, 220, 221, 300, 301, 310, 311, 320, 321, 400, 401, 410, 411, 420, 421, 1000, 1001, 1010, 1011, 1020, 1021, 1100, 1101, 1110, 1111, 1120, 1121, 1200, 1201, 1210, 1211, 1220, 1221, 1300, 1301, 1310, 1311

Offset

0,3

Comments

Places reading from right have values (1, 2, 6, 30, 210, ...) = primorials.

For n < 10 * 7# = 2100: a(n) = concatenation of n-th row in A235168 and for n > 0: A055642(a(n)) = A235224(n); for larger numbers the representation in A235168 is more appropriate. - Reinhard Zumkeller, Jan 05 2014

In the long run, numbers have fewer digits in the primorial base than in the factorial base (cf. A007623), since factorial(n) < n^n < primorial(n) for n > 12. However, the point where the digits become larger than 9 comes earlier: as soon as 10*7*5*3*2 = 2100 for the primorial base vs 10! = 3628800 in the factorial base. From there on, the representation using concatenation of digits written in decimal becomes ambiguous. - M. F. Hasler, Sep 22 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..2099

Index entries for sequences related to primorial base

Mathematica

Table[FromDigits@ IntegerDigits[n, MixedRadix[Reverse@ Prime@ Range@ 8]], {n, 0, 51}] (* Michael De Vlieger, Aug 23 2016, Version 10.2 *)

Prog

(Haskell)
a049345 n | n < 2100  = read $ concatMap show (a235168_row n) :: Int
          | otherwise = error "ambiguous primorial representation"
-- Reinhard Zumkeller, Jan 05 2014
(PARI) A049345(n, p=2) = if(n<p, n, A049345(n\p, nextprime(p+1))*10 + n%p) \\ Valid at least up to the point where digits > 9 would arise (n=10*7*5*3*2), thereafter the definition of the sequence is ambiguous. M. F. Hasler, Sep 22 2014
(Scheme)
(define (A049345 n) (if (>= n 2100) (error "A049345: ambiguous primorial representation when n is larger than 2099:" n) (let loop ((n n) (s 0) (t 1) (i 1)) (if (zero? n) s (let* ((p (A000040 i)) (d (modulo n p))) (loop (/ (- n d) p) (+ (* t d) s) (* 10 t) (+ 1 i)))))))
;; Antti Karttunen, Aug 26 2016
(Python)
from sympy import nextprime
def a(n, p=2):
    if n>2099: print("Error! Ambiguous primorial representation when n is larger than 2099")
    else: return n if n<p else a(n//p, nextprime(p))*10 + n%p
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 22 2017

Crossrefs

Cf. A000040, A002110 (primorials), A235168, A235224, A276086, A276150.

Cf. factorial base A007623.

Sequence in context: A261909 A325483 A235202 * A007623 A109827 A109839

Adjacent sequences: A049342 A049343 A049344 * A049346 A049347 A049348

Keyword

nonn,base,easy,nice

Author

R. K. Guy

Status

approved