A141709 -id:A141709 - cp's OEIS frontend

A062279 Smallest multiple k*n of n which is a palindrome or becomes a palindrome when 0's are added on the left (e.g. 10 becomes 010 which is a palindrome).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 60, 494, 70, 30, 80, 272, 90, 171, 20, 252, 22, 161, 600, 50, 494, 999, 252, 232, 30, 434, 800, 33, 272, 70, 252, 111, 494, 585, 40, 656, 252, 989, 44, 90, 414, 141, 2112, 343, 50, 969, 676, 212, 9990, 55, 616, 171, 232, 767

Offset: 0

Amarnath Murthy, Jun 17 2001

Every positive integer is a factor of a palindrome, unless it is a multiple of 10 (D. G. Radcliffe, see Links).

			a(13) = 494 is the smallest multiple of 13 which is a palindrome.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
P. De Geest, Smallest multipliers to make a number palindromic.

Cf. A050782, A062293. Values of k are given in A061674.

Cf. A141709.

: maxarg := 60; stop := 200000; for n := 0 to maxarg do k := 1; test := true; while test and k < stop do m := omit_trailzeros(n*k); if test := m <> int_reverse(m) then inc(k); end; end; if k < stop then write(n*k," "); else write(-1," "); end; end;

a062279 0 = 0
a062279 n = until ((== 1) . a136522 . a004151) (+ n) n
-- Reinhard Zumkeller, May 06 2013

A136522(A004151(a(n))) = 1. - Reinhard Zumkeller, May 06 2013

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Klaus Brockhaus, Jun 18 2001

A203070 Smallest positive multiple of n that is palindromic in base 3, ignoring trailing zeros.

Original entry on oeis.org

1, 2, 3, 4, 10, 6, 28, 8, 9, 10, 121, 12, 13, 28, 30, 16, 68, 18, 608, 20, 84, 242, 23, 24, 100, 26, 27, 28, 203, 30, 1550, 160, 363, 68, 280, 36, 1850, 608, 39, 40, 82, 84, 4988, 484, 90, 644, 1222, 48, 784, 100, 204, 52, 212, 54, 1210, 56, 1824, 1276, 1003

Offset: 1

Harvey P. Dale, Dec 28 2011

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A141709.

notpal3Q[i_]:=Module[{id=IntegerDigits[i,3]},While[Last[id]==0,id = Most[id]];id!=Reverse[id]]; lm3[n_]:=Module[{k=1},While[notpal3Q[k n],k++];k n]; Array[lm3,80]

A342582 a(n) is the least multiple of n that is a "binary antipalindrome" (i.e., an element of A035928).

Original entry on oeis.org

2, 2, 12, 12, 10, 12, 42, 56, 558, 10, 682, 12, 52, 42, 150, 240, 170, 558, 38, 240, 42, 682, 598, 240, 150, 52, 3132, 56, 232, 150, 558, 992, 8382, 170, 2730, 936, 666, 38, 936, 240, 738, 42, 3010, 3784, 535230, 598, 11938, 240, 2254, 150, 204, 52, 212, 3132

Offset: 1

Rémy Sigrist, Mar 15 2021

This sequence has similarities with A141709.

			For n = 42:
- 42 is a binary antipalindrome,
- so a(42) = 42.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A342582

Cf. A035928, A141709, A318569.

PARI
```
See Links section.
```

def comp(s): z, o = ord('0'), ord('1'); return s.translate({z:o, o:z})
def BCR(n): return int(comp(bin(n)[2:])[::-1], 2)
def bin_anti_pal(n): return BCR(n) == n
def a(n):
    kn = n
    while not bin_anti_pal(kn): kn += n
    return kn
print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Mar 15 2021

a(n) = n * A318569(n).

cp's OEIS Frontend

A062279 Smallest multiple k*n of n which is a palindrome or becomes a palindrome when 0's are added on the left (e.g. 10 becomes 010 which is a palindrome).

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A203070 Smallest positive multiple of n that is palindromic in base 3, ignoring trailing zeros.

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Author

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Links

Crossrefs

Programs

Mathematica

A342582 a(n) is the least multiple of n that is a "binary antipalindrome" (i.e., an element of A035928).

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

Formula