A067032 -id:A067032 - cp's OEIS frontend

A071265 Numbers which can be written in exactly two different ways as k + R(k) where R(k) is k reversed (A004086).

22, 33, 165, 176, 202, 222, 242, 262, 282, 302, 303, 322, 323, 342, 343, 362, 363, 382, 383, 403, 423, 443, 463, 483, 1515, 1535, 1555, 1575, 1595, 1615, 1616, 1635, 1636, 1655, 1656, 1675, 1676, 1695, 1696, 1716, 1736, 1756, 1776, 1796, 2002, 2871, 3003

Offset: 1

Amarnath Murthy, Jun 01 2002

The sums are unordered, so for example 12 + 21 is not counted as distinct from 21 + 12. - Sean A. Irvine, Jul 06 2024

			22 = 11 + 11 = 20 + 02, 202 =101 + 101 = 200 + 002.

Index entries for sequences related to Reverse and Add!

Cf. A071264, A071266, A067030, A067032, A067033, A067034.

More terms from Vladeta Jovovic and Klaus Brockhaus, Jun 03 2002

Offset corrected by Sean A. Irvine, Jul 06 2024

A067737 Integers n such that [number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the "Reverse and Add!" trajectory of k] is greater than [number of integers k such that n = k + reverse(k)].

Original entry on oeis.org

44, 66, 88, 110, 121, 132, 154, 176, 198, 242, 363, 404, 444, 484, 505, 524, 545, 564, 585, 605, 606, 625, 646, 665, 686, 707, 726, 747, 766, 787, 808, 827, 847, 848, 867, 888, 909, 928, 949, 968, 989, 1010, 1029, 1050, 1069, 1089, 1090, 1111, 1130, 1151

Offset: 1

Klaus Brockhaus, Feb 04 2002

Integers n such that n = A067030(j) for some j and A067284(j) > A067032(j).

			44 = A067030(13) is in the sequence, since there are five integers k (viz. 5, 13, 20, 31, 40; A067284(13) = 5) such that k is not of the form m + reverse(m) for any m and 44 occurs in the "Reverse and Add!" trajectory of k, but only four integers k (viz. 13, 22, 31, 40; A067032(13) = 4) such that 44 = k + reverse(k).

Index entries for sequences related to Reverse and Add!

Cf. A067030, A067031, A067032, A067284.

A068064 a(n) = number of integers k such that palindrome A068062(n) = k + reverse(k).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 9, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 1, 10, 3, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 4, 8, 12, 16, 20, 24

Offset: 1

Klaus Brockhaus, Feb 16 2002

The number of representations of a palindrome as a + b, where b = reverse(a); if a = reverse(b) and a is different from b, then a + b and b + a count as different representations.

			a(9) = 4, since A068062(9) = 44 and for k = 13, 22, 31, 40 we have 44 = k + reverse(k).
a(16) = 9, since A068062(16) = 121 and for k = 29, 38, 47, 56, 65, 74, 83, 92, 110 we have 121 = k + reverse(k).

Cf. A002113, A067030, A067032, A068062.

Offset corrected by Sean A. Irvine, Jan 23 2024

A358513 a(n) is the smallest number whose divisors include exactly n that can be written in the form m + reverse(m), for some m (A067030).

Original entry on oeis.org

1, 2, 4, 8, 12, 24, 48, 88, 220, 176, 132, 968, 264, 396, 528, 792, 1320, 1584, 2640, 3960, 5808, 5544, 8712, 14520, 11088, 24024, 21780, 36036, 40656, 39996, 53328, 87120, 60984, 72072, 205128, 132132, 121968, 144144, 293304, 199980, 266640, 439956, 264264, 360360, 733260, 396396, 660660, 799920

Offset: 0

Marius A. Burtea, Dec 04 2022

			1 has no divisors that can be written in the form m + reverse(m), so a(0) = 1.
2 has only the divisor 2 which is written 2 = 1 + reverse(1), so a(1) = 2.
3 has no divisors that can be written in the form m + reverse(m).
4 has divisors 1, 2, 4 but only 2 = 1 + reverse(1) and 4 = 2 + reverse(2), so a(2) = 4.
5 and 7 have no divisors that can be written in the form m + reverse(m), and 6 only has the divisors 2 = 2 + reverse(2) and 6 = 3 + reverse(3).
8 has divisors 1, 2, 4, 8 but only 2 = 1 + reverse(1), 4 = 2 + reverse(2) and 8 = 4 + reverse(4), so a(3) = 8.

Cf. A067032, A067030.

rev:=func; f:=func; a:=[]; for n in [0..25] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc:
S:= select(`<=`, map(t -> t + rev(t), {$1..10^6}),10^6):
V:= Array(0..49): count:= 0:
for n from 1 to 10^6 while count < 50 do
  v:= nops(numtheory:-divisors(n) intersect S);
  if v <= 49 and V[v] = 0 then
     count:= count+1; V[v]:= n;
  fi
od:
convert(V,list); # Robert Israel, Dec 28 2022

More terms from Robert Israel, Dec 28 2022

cp's OEIS Frontend

A071265 Numbers which can be written in exactly two different ways as k + R(k) where R(k) is k reversed (A004086).

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A067737 Integers n such that [number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the "Reverse and Add!" trajectory of k] is greater than [number of integers k such that n = k + reverse(k)].

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A068064 a(n) = number of integers k such that palindrome A068062(n) = k + reverse(k).

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A358513 a(n) is the smallest number whose divisors include exactly n that can be written in the form m + reverse(m), for some m (A067030).

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