A075466 Trajectory of 266718 under the Reverse and Add! operation carried out in base 4, written in base 10.

266718, 1017375, 2019150, 4934715, 20413980, 34239885, 64220175, 127195950, 321080475, 1286586060, 2154739965, 4288508415, 8571775230, 21401016315, 85781907180, 149736661725, 278082371775, 1369020907200, 1433193762225

Offset

0,1

Comments

266718 = A075421(358) is the smallest term > 318 of A075421 whose base 4 trajectory provably does not contain a palindrome. A proof along the lines of Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2, can be based on the formula given below. - The generating function given describes the sequence from a(26) onward; the g.f. for the complete sequence is known but more than twice as big.

Links

Table of n, a(n) for n=0..18.

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

Index entries for sequences related to Reverse and Add!

Formula

a(0), ..., a(18) as above; a(19) = 2780823717750; a(20) = 5492189757120; a(21) = 5749636151985; a(22) = 11156010444150; a(23) = 21968759028480; a(24) = 22226205423345; a(25) = 44109148986870; for n > 25 and n = 2 (mod 6): a(n) = 5*4^(2*k+14)-83865605*4^k where k = (n-2)/6; n = 3 (mod 6): a(n) = 5*4^(2*k+14)+3941683435*4^k-15 where k = (n-3)/6; n = 4 (mod 6): a(n) = 10*4^(2*k+14)+2515968150*4^k-10 where k = (n-4)/6; n = 5 (mod 6): a(n) = 20*4^(2*k+14)-335462420*4^k where k = (n-5)/6; n = 0 (mod 6): a(n) = 20*4^(2*k+14)+3690086620*4^k-15 where k = (n-6)/6; n = 1 (mod 6): a(n) = 40*4^(2*k+14)+2012774520*4^k-10 where k = (n-7)/6. G.f.: -15*(47049901525664*x^11+23708157972464*x^10+23433347158016*x^9-46912496118440*x^8-23502049861628*x^7-23433347158016*x^6-11908468626600*x^5-6137441522940*x^4-5862630708480*x^3+11771063219370*x^2+5931333412095*x+5862630708480)/((x-1)*(x^2+x+1)*(2*x^3-1)*(2*x^3+1)*(4*x^3-1))

Example

266718 (decimal) = 1001013132 -> 1001013132 + 2313101001 = 3320120133 = 1017375 (decimal).

Mathematica

NestWhileList[# + IntegerReverse[#, 4] &, 266718,  # !=
IntegerReverse[#, 4] &, 1, 23] (* Robert Price, Oct 18 2019 *)

Prog

(PARI) {m=266718; stop=19; c=0; while(c<stop, print1(k=m, ", "); rev=0; while(k>0, d=divrem(k, 4); k=d[1]; rev=4*rev+d[2]); c++; m=m+rev)}

Crossrefs

Cf. A075153, A075421, A075467.

Sequence in context: A263063 A043629 A234182 * A176384 A235821 A203793

Adjacent sequences: A075463 A075464 A075465 * A075467 A075468 A075469

Keyword

base,nonn

Author

Klaus Brockhaus, Sep 18 2002

Status

approved