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A076247 Trajectory of 1059774 under the Reverse and Add! operation carried out in base 4, written in base 10. 2
1059774, 4187583, 8355006, 20822715, 83391660, 144328605, 268919295, 1339676160, 1349598705, 2683144950, 5361370860, 9358549725, 17380163775, 85563883200, 89574690225, 173801637750, 343262166720, 359352580785 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

1059774 = A075421(1096) is the fourth term 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(16) onward; the g.f. for the complete sequence is known but nearly twice as big.

LINKS

Table of n, a(n) for n=0..17.

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

Index entries for sequences related to Reverse and Add!

FORMULA

a(0), ..., a(15) as above; for n > 15 and n = 4 (mod 6): a(n) = 5*4^(2*k+12)-5237765*4^k where k = (n+2)/6; n = 5 (mod 6): a(n) = 5*4^(2*k+12)+246174955*4^k-15 where k = (n+1)/6; n = 0 (mod 6): a(n) = 10*4^(2*k+12)+157132950*4^k-10 where k = n/6; n = 1 (mod 6): a(n) = 20*4^(2*k+12)-20951060*4^k where k = (n-1)/6; n = 2 (mod 6): a(n) = 20*4^(2*k+12)+230461660*4^k-15 where k = (n-2)/6; n = 3 (mod 6): a(n) = 40*4^(2*k+12)+125706360*4^k-10 where k = (n-3)/6. G.f.: -15*(185397326496*x^11+95559181296*x^10+91268404224*x^9-183251937960*x^8-92341098492*x^7 -91268404224*x^6-48628806952*x^5-27174921532*x^4-22884144448*x^3+46483418410*x^2 +23956838719*x+22884144448)/((x-1)*(x^2+x+1)*(2*x^3-1)*(2*x^3+1)*(4*x^3-1))

EXAMPLE

1059774 (decimal) = 10002232332 -> 10002232332 + 23323220001 = 33332112333 = 4187583 (decimal).

MATHEMATICA

NestWhileList[# + IntegerReverse[#, 4] &, 1059774,  # !=

IntegerReverse[#, 4] &, 1, 23] (* Robert Price, Oct 18 2019 *)

PROG

(PARI) {m=1059774; 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. A075421, A075153, A075466, A075467, A076248.

Sequence in context: A043679 A162893 A234089 * A076248 A234776 A081638

Adjacent sequences:  A076244 A076245 A076246 * A076248 A076249 A076250

KEYWORD

base,nonn

AUTHOR

Klaus Brockhaus, Oct 03 2002

STATUS

approved

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Last modified October 18 21:56 EDT 2021. Contains 348070 sequences. (Running on oeis4.)