A231720 a(0)=1, after which, for any n uniquely written as du*u! + ... + d2*2! + d1*1! (each di in range 0..i), a(n) = (du+1)*(u+1)! + ... + (d2+1)*3! + (d1+1)*2! + 1; the natural numbers with their factorial base representation (A007623) shifted left one step and each digit incremented by one, converted back to decimal.

1, 5, 15, 17, 21, 23, 57, 59, 63, 65, 69, 71, 81, 83, 87, 89, 93, 95, 105, 107, 111, 113, 117, 119, 273, 275, 279, 281, 285, 287, 297, 299, 303, 305, 309, 311, 321, 323, 327, 329, 333, 335, 345, 347, 351, 353, 357, 359, 393, 395, 399, 401, 405, 407, 417, 419

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

Formula

a(0)=1, and for n>=1, a(n) = A220655(A153880(n)).

Example

1 has a factorial base representation A007623(1) = '1'. This shifted once left is '10', and when each digit is incremented by one, this will be '21', and 2*2! + 1*1! = 5 (also A007623(5) = '21'), thus a(1)=5.
2 has a factorial base representation '10'. This shifted once left is '100', and with each digit incremented, makes '211'. 2*3! + 1*2! + 1*1! = 15, thus a(2)=15.

Prog

(Scheme)
;; Standalone iterative implementation:
(define (A231720 n) (let loop ((n n) (z 1) (i 2) (f 2)) (cond ((zero? n) z) (else (loop (quotient n i) (+ (* f (+ 1 (remainder n i))) z) (+ 1 i) (* f (+ i 1)))))))

Crossrefs

Subset of A227157. Cf. A007623, A153880, A220655.

Sequence in context: A065908 A297124 A166503 * A134453 A370919 A174598

Adjacent sequences: A231717 A231718 A231719 * A231721 A231722 A231723

Keyword

nonn,base

Author

Antti Karttunen, Nov 29 2013

Status

approved