A077441 In base 4, smallest number that requires n Reverse and Add! steps to reach a palindrome.

0, 4, 7, 26, 28, 127, 306, 348, 398, 301, 308, 203, 311, 783, 294, 350, 199, 296, 4268, 16595, 5326, 4253, 17399, 8235, 6189, 4270, 3107, 1270, 1532, 511, 67816, 65975, 24670, 12395, 4282, 3119, 28799, 16861, 18164, 66268, 45087, 71164, 309234

Offset

0,2

Comments

Base-4 analog of A066058 (base 2) and A023109 (base 10).

Links

Chai Wah Wu, Table of n, a(n) for n = 0..100

Index entries for sequences related to Reverse and Add!

Example

7 is the smallest number which requires two steps to reach a base 4 palindrome (cf. A075685), so a(2) = 5; 7 (decimal) = 13 -> 13 + 31 = 110 -> 110 + 011 = 121 (palindrome) = 25 (decimal).

Prog

(PARI) {m=46; v=[]; for(j=1, m+1, v=concat(v, -1)); mc=m+1; n=0; while(mc>0, a=-1; c=0; k=n; while(c<m+1, q=k; rev=0; while(q>0, d=divrem(q, 4); q=d[1]; rev=4*rev+d[2]); if(k==rev, a=c; c=m+1, c++; k=k+rev)); if(0<=a&&a<=m, if(v[a+1]<0, v[a+1]=n; mc--; print1([a, n]))); n++); print(); for(j=1, m+1, print1(v[j], ", "))}
(Python)
from gmpy2 import digits
def A077441(n):
....if n > 0:
........k = 0
........while True:
............m = k
............for i in range(n):
................s = digits(m, 4)
................if s == s[::-1]:
....................break
................m += int(s[::-1], 4)
............else:
................s = digits(m, 4)
................if s == s[::-1]:
....................return k
............k += 1
....else:
........return 0 # Chai Wah Wu, Jan 17 2015

Crossrefs

Cf. A075685, A066058, A023109.

Sequence in context: A211942 A110413 A075686 * A269744 A303844 A197789

Adjacent sequences: A077438 A077439 A077440 * A077442 A077443 A077444

Keyword

base,nonn

Author

Klaus Brockhaus, Nov 05 2002

Status

approved