A033621 Numbers k such that k-1 is a palindrome in base 10, and k+1 is a palindrome in base 17.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 89, 233, 374, 425, 596, 647, 869, 920, 3444, 4775, 23633, 45755, 62027, 180082, 231133, 310014, 487785, 566666, 645547, 724428, 803309, 1027202, 1064602, 1215122, 1252522, 1403042, 80399309, 111222112, 112060212, 146979642

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..61

Example

a(12) = 89 is a term because 89-1 = 88 is a palindrome in base 10, while 89+1 = 55_17 is a palindrome in base 17. - Robert Israel, Jan 14 2026

Maple

digrev:= proc(n, b) local L, i;
  L:= convert(n, base, b);
  add(L[-i]*b^(i-1), i=1..nops(L))
end proc:
b1:= 10: b2:= 17:
R:= $1..10, 12: count:= 12:
for d from 2 while count < 50 do
  if d::even then
    for x from b2^(d/2-1) to b2^(d/2)-1 while count < 50 do
      m:= x*b2^(d/2)+digrev(x, b2);
      if digrev(m-2, b1) = m-2 then
         R:= R, m-1; count:= count+1;
      fi
    od
  else
    for x from b2^((d-3)/2) to b2^((d-1)/2)-1 while count < 50 do
      for y from 0 to b2-1 do
        m:= x*b2^((d+1)/2)+y*b2^((d-1)/2) + digrev(x, b2);
        if digrev(m-2, b1) = m-2 then
          R:= R, m-1; count:= count+1;
        fi
    od od
  fi
od:
R; # Robert Israel, Jan 14 2026

Prog

(PARI) isok(m) = my(da=digits(m-1, 10), db=digits(m+1, 17)); da==Vecrev(da) && db==Vecrev(db); \\ Michel Marcus, Jul 09 2020

Crossrefs

Sequence in context: A061729 A286126 A249157 * A332808 A108548 A333692

Adjacent sequences: A033618 A033619 A033620 * A033622 A033623 A033624

Keyword

nonn,base

Author

Olivier Gérard

Extensions

More terms from Michel ten Voorde

Corrected and extended by Sean A. Irvine, Jul 08 2020

Status

approved