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

Author

Klaus Brockhaus, Nov 05 2002

Keywords

• base
• nonn

Comments

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

Examples

			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).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..100
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A075685, A066058, A023109.

Programs

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(c0,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