A030103 Base 4 reversal of n (written in base 10).

0, 1, 2, 3, 1, 5, 9, 13, 2, 6, 10, 14, 3, 7, 11, 15, 1, 17, 33, 49, 5, 21, 37, 53, 9, 25, 41, 57, 13, 29, 45, 61, 2, 18, 34, 50, 6, 22, 38, 54, 10, 26, 42, 58, 14, 30, 46, 62, 3, 19, 35, 51, 7, 23, 39, 55, 11, 27, 43, 59, 15, 31, 47, 63, 1, 65, 129, 193, 17, 81, 145, 209, 33, 97, 161

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• look
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004086, A030101 - A030108, A048703, A055948, A035524.

Programs

Haskell

import Data.List (unfoldr)
a030103 n = foldl (\v d -> 4*v + d) 0 $ unfoldr dig n where
    dig x = if x == 0 then Nothing else Just $ swap $ divMod x 4
-- Reinhard Zumkeller, Oct 10 2011

Mathematica

IntegerReverse[Range[0, 100], 4] (* Paolo Xausa, Aug 07 2024 *)

PARI

a(n,b=4)=subst(Polrev(base(n,b)),x,b) /* where */
base(n,b)={my(a=[n%b]);while(0M. F. Hasler, Nov 04 2011
(MIT/GNU Scheme)
(define (A030103 n) (if (zero? n) n (let ((uplim (+ (A000523 n) (- 1 (modulo (A000523 n) 2))))) (add (lambda (i) (* (bit_i n (+ i (expt -1 i))) (expt 2 (- uplim i)))) 0 uplim))))
(define (bit_i n i) (modulo (floor->exact (/ n (expt 2 i))) 2))
;; The functional add implements sum_{i=lowlim..uplim} intfun(i):
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
;; Antti Karttunen, Oct 30 2013