|
Search: id:A077077
|
|
|
| A077077 |
|
Trajectory of 775 under the Reverse and Add! operation carried out in base 2, written in base 10. |
|
+0
2
|
|
| 775, 1674, 2325, 5022, 8919, 23976, 26757, 47376, 49581, 96048, 102669, 193056, 197469, 388704, 401949, 779328, 788157, 1563840, 1590333, 3131520, 3149181, 6273408, 6326397, 12554496, 12589821, 25129728, 25235709, 50274816, 50345469
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
The base 2 trajectory of 775 = A075252(4) provably does not contain a palindrome. A proof along the lines of K. Brockhaus, On the 'Reverse and Add!' algorithm in base 2, can be based on the formula given below.
|
|
LINKS
|
K. Brockhaus, On the 'Reverse and Add!' algorithm in base 2
Index entries for sequences related to Reverse and Add!
|
|
FORMULA
|
a(0), ..., a(5) as above; for n >5 and n = 2 (mod 4): a(n) = 3*2^(2*k+7)+273*2^k-3 where k = (n+6)/4; n = 3 (mod 4): a(n) = 6*2^(2*k+7)-222*2^k where k = (n+5)/4; n = 0 (mod 4): a(n) = 6*2^(2*k+7)+54*2^k-3 where k = (n+4)/4; n = 1 (mod 4): a(n) = 12*2^(2*k+7)-282*2^k where k = (n+3)/4. G.f.: (2112*x^13-14328*x^12-28680*x^11+1860*x^10+22644*x^9+19840*x^8+14508*x^7-4650*x^6 -8910*x^5-1944*x^4-1674*x-775)/((x-1)*(x+1)*(2*x^2-1)*(2*x^4-1))
|
|
EXAMPLE
|
775 (decimal) = 1100000111 -> 1100000111 + 1110000011 = 11010001010 = 1674 (decimal).
|
|
PROGRAM
|
(PARI) {m=775; stop=30; c=0; while(c<stop, print1(k=m, ", "); rev=0; while(k>0, d=divrem(k, 2); k=d[1]; rev=2*rev+d[2]); c++; m=m+rev)}
|
|
CROSSREFS
|
Cf. A075252, A061561, A075253, A075268, A077076.
Adjacent sequences: A077074 A077075 A077076 this_sequence A077078 A077079 A077080
Sequence in context: A133964 A033919 A055521 this_sequence A043519 A043384 A008746
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 25 2002
|
|
|
Search completed in 0.002 seconds
|
