A052008 -id:A052008 - cp's OEIS frontend

A056964 a(n) = n + reversal of digits of n.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 66, 77, 88, 99, 110

Offset: 0

Henry Bottomley, Jul 18 2000

If n has an even number of digits then a(n) is a multiple of 11.

Also called the Reverse and Add!, or RADD operation. Iteration of this function leads to the definition of Lychrel and related numbers, cf. A023108, A063048, A088753, A006960, and many others. - M. F. Hasler, Apr 13 2019

			a(17) = 17 + 71 = 88.

Indranil Ghosh, Table of n, a(n) for n = 0..20000 (first 1001 terms from T. D. Noe)
Eric Weisstein's World of Mathematics, Reverse-Then-Add Sequence
Index entries for sequences related to Reverse and Add!

Cf. A004086, A056965, A067030.
Differs from A052008 when n=101 and a(101)=202 while A052008(101)=121
Cf. A036839.

a056964 n = n + a004086 n  -- Reinhard Zumkeller, Oct 14 2011

Table[n+FromDigits[Reverse[IntegerDigits[n]]],{n,0,100}] (* Harvey P. Dale, Jul 19 2014 *)
#+IntegerReverse[#]&/@Range[0,100] (* Harvey P. Dale, Jul 31 2025 *)

A056964(n)=fromdigits(Vecrev(digits(n)))+n \\ Charles R Greathouse IV, Oct 28 2014

def A056964(n): return n+int(str(n)[::-1]) # Indranil Ghosh, Jan 29 2017

a(n) = n + A004086(n) = 2*n - A056965(n).

n < a(n) < 11n for n > 0. - Charles R Greathouse IV, Nov 17 2022

A319747 a(n) = A319726(n) + A319657(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 10, 20, 30, 40, 50, 60, 70, 80, 90, 20, 30, 40, 50, 60, 70, 80, 90, 100, 30, 40, 50, 60, 70, 80, 90, 100, 110, 40, 50, 60, 70, 80, 90, 100, 110, 120, 50, 60, 70, 80, 90, 100, 110, 120, 130, 60, 70, 80, 90, 100, 110, 120, 130, 140, 70

Offset: 0

Seiichi Manyama, Sep 27 2018

This sequence is different from A055958. For example, A055958(82) = 164 and a(82) = 100.

Seiichi Manyama, Table of n, a(n) for n = 0..6560

Base b: A319785 (b=2), this sequence (b=9), A052008 (b=10).

Cf. A055958, A165110, A319657, A319726.

Table[FromDigits[Reverse[#], 9] + FromDigits[#, 9] & [Sort[IntegerDigits[n, 9]]], {n, 0, 100}] (* Paolo Xausa, Aug 08 2024 *)

a(n) = my(dn=digits(n, 9)); fromdigits(vecsort(dn), 9) + fromdigits(vecsort(dn,,4), 9); \\ Michel Marcus, Sep 28 2018

A319785 a(n) = A073138(n) + A038573(n).

Original entry on oeis.org

0, 2, 3, 6, 5, 9, 9, 14, 9, 15, 15, 21, 15, 21, 21, 30, 17, 27, 27, 35, 27, 35, 35, 45, 27, 35, 35, 45, 35, 45, 45, 62, 33, 51, 51, 63, 51, 63, 63, 75, 51, 63, 63, 75, 63, 75, 75, 93, 51, 63, 63, 75, 63, 75, 75, 93, 63, 75, 75, 93, 75, 93, 93, 126, 65, 99, 99, 119

Offset: 0

Seiichi Manyama, Sep 27 2018

This sequence is different from A055944. For example, A055944(5) = 10 and a(5) = 9.

Seiichi Manyama, Table of n, a(n) for n = 0..8191

Base b: this sequence (b=2), A319803 (b=3), A319804 (b=4), A319805 (b=5), A319806 (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A038573, A055944, A073138.

Table[FromDigits[Reverse[#], 2] + FromDigits[#, 2] & [Sort[IntegerDigits[n, 2]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(dn=binary(n)); fromdigits(vecsort(dn), 2) + fromdigits(vecsort(dn,,4), 2); \\ Michel Marcus, Sep 28 2018

A319803 a(n) = A319651(n) + A038574(n).

Original entry on oeis.org

0, 2, 4, 4, 8, 12, 8, 12, 16, 10, 16, 26, 16, 26, 36, 26, 36, 42, 20, 26, 32, 26, 36, 42, 32, 42, 52, 28, 40, 68, 40, 52, 80, 68, 80, 92, 40, 52, 80, 52, 80, 108, 80, 108, 120, 68, 80, 92, 80, 108, 120, 92, 120, 132, 56, 68, 80, 68, 80, 92, 80, 92, 104, 68, 80, 92, 80, 108, 120, 92, 120, 132, 80, 92

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055946.

Seiichi Manyama, Table of n, a(n) for n = 0..6560

Base b: A319785 (b=2), this sequence (b=3), A319804 (b=4), A319805 (b=5), A319806 (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055946, A038574, A319651.

Table[FromDigits[Reverse[#], 3] + FromDigits[#, 3] & [Sort[IntegerDigits[n, 3]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 3)); fromdigits(vecsort(nd), 3) + fromdigits(vecsort(nd,,4), 3); \\ Michel Marcus, Sep 28 2018

A319804 a(n) = A319720(n) + A319652(n).

Original entry on oeis.org

0, 2, 4, 6, 5, 10, 15, 20, 10, 15, 20, 25, 15, 20, 25, 30, 17, 25, 42, 59, 25, 42, 59, 76, 42, 59, 67, 84, 59, 76, 84, 92, 34, 42, 50, 67, 42, 59, 67, 84, 50, 67, 84, 101, 67, 84, 101, 109, 51, 59, 67, 75, 59, 76, 84, 92, 67, 84, 101, 109, 75, 92, 109, 126, 65, 85, 150, 215

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055948.

Seiichi Manyama, Table of n, a(n) for n = 0..4095

Base b: A319785 (b=2), A319803 (b=3), this sequence (b=4), A319805 (b=5), A319806 (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055948, A319652, A319720.

Table[FromDigits[Reverse[#], 4] + FromDigits[#, 4] & [Sort[IntegerDigits[n, 4]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 4)); fromdigits(vecsort(nd), 4) + fromdigits(vecsort(nd,,4), 4); \\ Michel Marcus, Sep 28 2018

A319805 a(n) = A319722(n) + A319653(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 6, 12, 18, 24, 30, 12, 18, 24, 30, 36, 18, 24, 30, 36, 42, 24, 30, 36, 42, 48, 26, 36, 62, 88, 114, 36, 62, 88, 114, 140, 62, 88, 98, 124, 150, 88, 114, 124, 134, 160, 114, 140, 150, 160, 170, 52, 62, 72, 98, 124, 62, 88, 98, 124, 150, 72, 98, 124, 150, 176

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055950.

Seiichi Manyama, Table of n, a(n) for n = 0..3124

Base b: A319785 (b=2), A319803 (b=3), A319804 (b=4), this sequence (b=5), A319806 (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055950, A319653, A319722.

a:= n-> (l-> add((l[i]+l[-i])*5^(i-1), i=1..nops(l)))(sort(convert(n, base, 5))):
seq(a(n), n=0..64);  # Alois P. Heinz, Aug 07 2024

Table[FromDigits[Reverse[#], 5] + FromDigits[#, 5] & [Sort[IntegerDigits[n, 5]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 5)); fromdigits(vecsort(nd), 5) + fromdigits(vecsort(nd,,4), 5); \\ Michel Marcus, Sep 28 2018

A319806 a(n) = A319723(n) + A319654(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 7, 14, 21, 28, 35, 42, 14, 21, 28, 35, 42, 49, 21, 28, 35, 42, 49, 56, 28, 35, 42, 49, 56, 63, 35, 42, 49, 56, 63, 70, 37, 49, 86, 123, 160, 197, 49, 86, 123, 160, 197, 234, 86, 123, 135, 172, 209, 246, 123, 160, 172, 184, 221, 258, 160, 197, 209, 221, 233

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055952.

Seiichi Manyama, Table of n, a(n) for n = 0..7775

Base b: A319785 (b=2), A319803 (b=3), A319804 (b=4), A319805 (b=5), this sequence (b=6), A319807 (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055952, A319654, A319723.

Table[FromDigits[Reverse[#], 6] + FromDigits[#, 6] & [Sort[IntegerDigits[n, 6]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 6)); fromdigits(vecsort(nd), 6) + fromdigits(vecsort(nd,,4), 6); \\ Michel Marcus, Sep 28 2018

A319807 a(n) = A319724(n) + A319655(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 8, 16, 24, 32, 40, 48, 56, 16, 24, 32, 40, 48, 56, 64, 24, 32, 40, 48, 56, 64, 72, 32, 40, 48, 56, 64, 72, 80, 40, 48, 56, 64, 72, 80, 88, 48, 56, 64, 72, 80, 88, 96, 50, 64, 114, 164, 214, 264, 314, 64, 114, 164, 214, 264, 314, 364, 114, 164, 178, 228

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055954.

Seiichi Manyama, Table of n, a(n) for n = 0..2400

Base b: A319785 (b=2), A319803 (b=3), A319804 (b=4), A319805 (b=5), A319806 (b=6), this sequence (b=7), A319808 (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055954, A319655, A319724.

Table[FromDigits[Reverse[#], 7] + FromDigits[#, 7] & [Sort[IntegerDigits[n, 7]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 7)); fromdigits(vecsort(nd), 7) + fromdigits(vecsort(nd,,4), 7); \\ Michel Marcus, Sep 28 2018

A319808 a(n) = A319725(n) + A319656(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 9, 18, 27, 36, 45, 54, 63, 72, 18, 27, 36, 45, 54, 63, 72, 81, 27, 36, 45, 54, 63, 72, 81, 90, 36, 45, 54, 63, 72, 81, 90, 99, 45, 54, 63, 72, 81, 90, 99, 108, 54, 63, 72, 81, 90, 99, 108, 117, 63, 72, 81, 90, 99, 108, 117, 126, 65, 81, 146, 211

Offset: 0

Seiichi Manyama, Sep 28 2018

This sequence is different from A055956.

Seiichi Manyama, Table of n, a(n) for n = 0..4095

Base b: A319785 (b=2), A319803 (b=3), A319804 (b=4), A319805 (b=5), A319806 (b=6), A319807 (b=7), this sequence (b=8), A319747 (b=9), A052008 (b=10).

Cf. A055956, A319656, A319725.

Table[FromDigits[Reverse[#], 8] + FromDigits[#, 8] & [Sort[IntegerDigits[n, 8]]], {n, 0, 100}] (* Paolo Xausa, Aug 07 2024 *)

a(n) = my(nd=digits(n, 8)); fromdigits(vecsort(nd), 8) + fromdigits(vecsort(nd,,4), 8); \\ Michel Marcus, Sep 28 2018

A345111 a(n) = n + A345110(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 66, 77, 88

Offset: 0

Felix Fröhlich, Jun 09 2021

First differs from both A052008 and A056964 at n = 101.

			For n = 101: 101 + A345110(101) = 101 + 11 = 112, so a(101) = 112.

Cf. A052008, A056964, A345110, A345112, A345113, A345114, A345115.

Array[#+FromDigits@RotateLeft@IntegerDigits@#&,100,0] (* Giorgos Kalogeropoulos, Jun 09 2021 *)

eva(n) = subst(Pol(n), x, 10)
rot(vec) = if(#vec < 2, return(vec)); my(s=concat(Str(2), ".."), v=[]); s=concat(s, Str(#vec)); v=vecextract(vec, s); v=concat(v, vec[1]); v
a(n) = n + eva(rot(digits(n)))

def rotl(s): return s[1:] + s[0]
def a(n): return n + int(rotl(str(n)))
print([a(n) for n in range(63)]) # Michael S. Branicky, Jun 09 2021

cp's OEIS Frontend

A056964 a(n) = n + reversal of digits of n.

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A319747 a(n) = A319726(n) + A319657(n).

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A319785 a(n) = A073138(n) + A038573(n).

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A319803 a(n) = A319651(n) + A038574(n).

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A319804 a(n) = A319720(n) + A319652(n).

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A319805 a(n) = A319722(n) + A319653(n).

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A319806 a(n) = A319723(n) + A319654(n).

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A319807 a(n) = A319724(n) + A319655(n).

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