A065208 Three 'Reverse and Add' steps are needed to reach a palindrome.

59, 68, 86, 95, 155, 156, 157, 158, 164, 165, 168, 178, 180, 184, 185, 186, 194, 199, 249, 254, 255, 256, 257, 263, 264, 267, 277, 283, 284, 285, 293, 298, 299, 348, 349, 354, 355, 356, 362, 366, 376, 382, 384, 389, 392, 397, 398, 399, 439, 447, 448, 449, 452, 453, 455, 461, 462, 465, 475, 481, 482, 483, 488, 489, 491, 496, 497, 498, 499, 538, 546, 547, 548, 551, 552, 553, 554, 560, 561, 564, 574, 580, 581, 582, 587, 588, 590, 596, 597, 598, 637, 645, 647, 650, 651, 652, 653, 660, 663, 673, 680, 681, 687, 694, 695, 697, 736, 744, 745, 746, 750

Offset

1,1

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded.

Links

Harry J. Smith, Table of n, a(n) for n=1,...,1000

Index entries for sequences related to Reverse and Add!

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]
tst[n_]:=palQ/@NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&, n, 3]=={False, False, False, True}
Select[Range[750], tst] (* Harvey P. Dale, Nov 26 2010 *)

Prog

(ARIBAS): revadd_steps(3, 54). For the definition of function revadd_steps see A065206.
(PARI) Rev(x)= { local(d, r=0); while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); return(r) } digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } Palin(x)= { local(d, e, f, i, t, y); if (x==0, return(1)); y=x; d=digitsIn(x); t=10^(d - 1); for (i=1, d\2, f=y-10*(y\10); y\=10; e=x\t; x-=t*e; t/=10; if (e!=f, return(0)) ); return(1) } { n=0; for (m = 0, 10^9, p=m; b=1; for (i=1, 3, if (Palin(p), b=0; break); p=Rev(p) + p); if (b && Palin(p), write("b065208.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 14 2009

Crossrefs

A002113, A015979, A065206.

Sequence in context: A216872 A235225 A015979 * A061759 A061764 A316971

Adjacent sequences: A065205 A065206 A065207 * A065209 A065210 A065211

Keyword

nonn,base

Author

Klaus Brockhaus, Oct 21 2001

Extensions

OFFSET changed from 0,1 to 1,1 by Harry J. Smith, Oct 14 2009

More terms from Harvey P. Dale, Nov 26 2010

Status

approved