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A049345
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n written in primorial base.
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42
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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
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listen;
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internal format)
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..2099
Index entries for sequences related to primorial base
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MATHEMATICA
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Table[FromDigits@ IntegerDigits[n, MixedRadix[Reverse@ Prime@ Range@ 8]], {n, 0, 51}] (* Michael De Vlieger, Aug 23 2016, Version 10.2 *)
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PROG
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(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 prime
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(int(n/p), nextprime(p))*10 + n%p
print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 22 2017
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CROSSREFS
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Cf. A000040, A002110 (primorials), A235168, A235224, A276086, A276150.
Cf. factorial base A007623.
Sequence in context: A197652 A261909 A235202 * A007623 A109827 A109839
Adjacent sequences: A049342 A049343 A049344 * A049346 A049347 A049348
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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R. K. Guy
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STATUS
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approved
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