0,1

22, 77 and 442 are the first terms of A075252. The base 2 trajectory of 442 is completely different from the trajectories of 22 (cf. A061561) and 77 (cf. A075253). Using the formula given below one can prove that it does not contain a palindrome (cf. Links). - The generating function given describes the sequence from a(36) onward; the g.f. for the complete sequence is known but about five times as big.

K. Brockhaus, On the 'Reverse and Add!' algorithm in base 2

Index entries for sequences related to Reverse and Add!

a(0), ..., a(28) as above; a(29) = 703932681; a(30) =1310348526; a(31) = 2309980455; a(32) = 6143702712; a(33) = 7131271077; a(34) = 12699398352; a(35) = 13441412493; for n > 35 and n = 0 (mod 4): a(n) = 3*2^(2*k+23)-12576771*2^k where k = (n-16)/4; n = 1 (mod 4): a(n) = 3*2^(2*k+23)+12576771*2^k-3 where k = (n-17)/4; n = 2 (mod 4): a(n) = 6*2^(2*k+23)-12576771*2^k where k = (n-18)/4; n = 3 (mod 4): a(n) = 6*2^(2*k+23)+37730313*2^k-3 where k = (n-19)/4. G.f.: -3*(17984782524*x^7+16911564736*x^6-18118934750*x^5-17045716960*x^4-8589934590*x^3-8321630144*x^2+8724086815*x+8455782368)/((x-1)*(x+1)*(2*x^2-1)*(2*x^4-1)).

442 (decimal) = 110111010 -> 110111010 + 010111011 = 1001110101 = 629 (decimal).

(PARI) {m=442; stop=29; 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)}

Cf. A058042, A061561, A075252, A075253.

Sequence in context: A110996 A013769 A013899 this_sequence A031609 A031720 A069106

Adjacent sequences: A075265 A075266 A075267 this_sequence A075269 A075270 A075271

base,nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 11 2002