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A241213 a(n) is built digit-by-digit (see comments for details). 1
1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 114, 115, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 140, 141, 142, 143, 144, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is built digit-by-digit as a_i ... a_3 a_2 a_1.

Note that in this case, the definition of digit is a nonnegative integer. If i > 3, number digits of a_i may be greater than 1.

Successively, we have:

a_1 = n mod 6;

a_2 = ((n - a_1)/primorial(2)) mod prime(2+1);

a_3 = ((n - a_1 - a_2*primorial(2))/primorial(3)) mod prime(3+1);

...

a_i = ((n - a_1 - a_2*primorial(2)-...-a_(i-1)*primorial(i-1))/primorial(i)) mod prime(i+1).

So that finally, n = a_1 + a_2*primorial(2) + ... + a_i*primorial(i).

LINKS

Lear Young, Table of n, a(n) for n = 1..100000

EXAMPLE

a(2287) = 10611.

10611 is built digit-by-digit as a_4 a_3 a_2 a_1 = 10 6 1 1.

And a_1+a_2*primorial(2)+a_3*primorial(3)+a_4*primorial(4) = 1 + 1*6 + 6*30 + 10*210 = 2287.

(Definition of digit is nonnegative integer. See comments for how to get a_1, a_2, a_3, a_4.)

PROG

(Sage)

Pr = Primes()

c = oeis(2110)[:10]

def bjz(a):

    d = len(str(a)) + 1

    b  = [0] * (d)

    b[0] = a % 6

    s = 0

    for x in range(1, d):

        if x > 1:

            s += c[x] * b[x-1]

        b[x] = ((a - b[0] - s) / c[x+1] ) % Pr.unrank(x+1)

    return int(''.join(map(str, b[::-1])))

[ bjz(x)  for x in range(1, 101)] # Lear Young, Apr 17 2014

CROSSREFS

Sequence in context: A266117 A037473 A007092 * A047596 A199502 A089964

Adjacent sequences:  A241210 A241211 A241212 * A241214 A241215 A241216

KEYWORD

nonn,base

AUTHOR

Lear Young, Apr 17 2014

STATUS

approved

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Last modified June 20 16:26 EDT 2019. Contains 324234 sequences. (Running on oeis4.)