A055161 -id:A055161 - cp's OEIS frontend

A055162 The number n has digits in ascending order and n=a-b where a has the digits of n in descending order and b has the digits of n in another order (a and b perhaps with extra zeros), ordered by a.

459, 1467, 445599, 134667, 13346667, 1245789, 123456789, 444555999, 1333466667, 123456789, 12457899, 12334566789, 133334666667, 12334566789, 1234567899, 124578999, 444455559999, 1233345666789

Offset: 1

Henry Bottomley, Apr 27 2000

Each term of this sequence A055162(n) corresponds to A099009(n+1), with its digits being reordered in the ascending manner. - Alexander R. Povolotsky, Apr 26 2012

All terms of this sequence are divisible by nine, yielding 51, 163, 49511, 14963, 1482963,.... - Alexander R. Povolotsky, Apr 29 2012

			459 = 954 - 495.

Denis Borris, Ken Duisenberg's Puzzle of the Week, April 20, 2000

Source

Cf. A055159, A099009.

a(n) = A055161(n) - A055160(n).

A055160 Numbers n with the property that n=a-b where a has the digits of n in descending order and b has the digits of n in ascending order (perhaps with leading zeros), ordered by a.

Original entry on oeis.org

495, 6174, 549945, 631764, 63317664, 97508421, 864197532, 554999445, 6333176664, 9753086421, 9975084201, 86431976532, 633331766664, 975330866421, 997530864201, 999750842001, 555499994445, 8643319766532

Offset: 1

Henry Bottomley, Apr 27 2000

This sequence appears to differ from A099009 at the positions of two terms in it: 554999445 and 555499994445. - Alexander R. Povolotsky, May 01 2012

			495 = 954-459.

Denis Borris, Ken Duisenberg's Puzzle of the Week, April 20, 2000

Denis Borris, Ken Duisenberg's Puzzle of the Week, April 20, 2000
Yutaka Nishiyama, The weirdness of number 6174, International Journal of Pure and Applied Mathematicsm, Volume 80 No. 3 2012, 363-373. - From _N. J. A. Sloane_, Oct 29 2014

Cf. A055157, A099009.

a(n) = A055161(n) - A055162(n).

A055158 n has distinct digits in descending order and n=a+b where a has the digits of n in another order and b has the digits of n in ascending order (perhaps with leading zeros).

Original entry on oeis.org

954, 7641, 98754210, 987654321, 9876543210

Offset: 0

Henry Bottomley, Apr 27 2000

			954=495+459

Denis Borris, Ken Duisenberg's Puzzle of the Week, April 20, 2000

Source

Cf. A055161.

a(n)= A055157(n)+A055159(n)

A121969 Numbers k such that if you subtract k-reversed from k you get a natural number with the same digits as k.

Original entry on oeis.org

954, 1980, 2961, 3870, 5823, 7641, 9108, 19980, 29880, 29961, 32760, 38970, 39780, 49680, 49842, 54270, 58923, 59580, 60273, 60732, 69462, 69480, 69723, 70254, 73260, 76941, 79344, 79380, 89226, 89280, 89604, 90810, 91908, 96732, 99108

Offset: 1

Tanya Khovanova, Sep 04 2006

			954 - 459 = 495, 19980 - 8991 = 10989.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 154 (entry for 1980).

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

Cf. A055161.

srdQ[n_]:=Module[{idn=IntegerDigits[n],rn},rn=FromDigits[Reverse[idn]];n>rn&&Sort[IntegerDigits[n-rn]]==Sort[idn]]; Select[Range[100000], srdQ] (* Harvey P. Dale, Jun 21 2013 *)

isok(n) = {my(d = digits(n)); diff = my(n - subst(Polrev(d), x, 10)); (diff > 0) && (vecsort(digits(diff)) == vecsort(d));} \\ Michel Marcus, Sep 04 2015

A121970 Numbers k such that if you subtract k from its reversal you get a positive number with the same digits as k.

Original entry on oeis.org

459, 1467, 1692, 3285, 8019, 14967, 16992, 23706, 23769, 24894, 26496, 32796, 32985, 37206, 40698, 44397, 45207, 49599, 62298, 80199, 80919, 104697, 106992, 108729, 108972, 127809, 134667, 135378, 135774, 136818, 136962, 145827, 147492

Offset: 1

Tanya Khovanova, Sep 04 2006

If negative numbers are included then the sequence is the above together with its reversals. - Robert G. Wilson v, Sep 11 2006

			459 is a member because 954 - 459 = 495; 16992 is a member because 29961 - 16992 = 12969.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Kevin Browne, Subtracting the Reversal.

Cf. A055161, A121969.

Select[Table[n, {n, 200000}], ToExpression[StringReverse[ToString[ # ]]] - # > 0 && Sort[IntegerDigits[ # ]] == Sort[IntegerDigits[ToExpression[StringReverse[ToString[ # ]]] - # ]] &]
fQ[n_] := Block[{id = IntegerDigits@n}, rev = FromDigits@ Reverse@id; rev > n && Sort@id == Sort@IntegerDigits[rev - n]]; Select[ Range@153971, fQ@# &] (* Robert G. Wilson v, Sep 11 2006 *)
Select[Range[150000],With[{c=IntegerReverse[#]-#},c>0&&Sort[IntegerDigits[c]]==Sort[IntegerDigits[#]]&]] (* Harvey P. Dale, Jun 07 2025 *)

A331468 Lexicographically earliest sequence of distinct triples (A,B,C) such that A + B = C with A, B, C anagrams of each other and A < B.

Original entry on oeis.org

459, 495, 954, 1089, 8019, 9108, 1089, 8091, 9180, 1269, 1692, 2961, 1467, 6147, 7614, 1467, 6174, 7641, 1476, 4671, 6147, 1503, 3510, 5013, 1530, 3501, 5031, 1746, 4671, 6417, 2385, 2853, 5238, 2439, 2493, 4932, 2502, 2520, 5022, 2538, 3285, 5823, 2691, 6921, 9612, 2853, 5382, 8235, 3285, 5238, 8523

Offset: 1

Eric Angelini and Gilles Esposito-Farèse, Jan 17 2020

The sequence is infinite as (10*A,10*B,10*C) is a legal triple if (A,B,C) is a legal triple.
From Bernard Schott, Jan 19 2020: (Start)
Theorem: Every term of this sequence is divisible by 9.
Proof: If m = digsum(A) = digsum(B) = digsum(C) where digsum = A007953, then A + B = C implies digsum(A) + digsum(B) == digsum(C) (mod 9), so 2*m == m (mod 9) and m == 0 (mod 9). (End)
The numbers of 3-digit to 8-digit triples are: 1, 25, 648, 17338, 495014, and 17565942. - Hans Havermann, Feb 02 2020

			The first triple is (459,495,954) and we have 459 + 495 = 954, anagrams of each other;
The second triple is (1089,8019,9108) and we have 1089 + 8019 = 9108, anagrams of each other;
The third triple is (1089,8091,9180) and we have 1089 + 8091 = 9180, anagrams of each other;
The fourth triple is (1269,1692,2961) and we have 1269 +1692 = 2961, anagrams of each other; etc.

Gilles Esposito-Farèse, Table of n, a(n) for n = 1..50000

Cf. A160851, A203024, A121969, A055160, A055161, A055162.

cp's OEIS Frontend

A055162 The number n has digits in ascending order and n=a-b where a has the digits of n in descending order and b has the digits of n in another order (a and b perhaps with extra zeros), ordered by a.

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A055160 Numbers n with the property that n=a-b where a has the digits of n in descending order and b has the digits of n in ascending order (perhaps with leading zeros), ordered by a.

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A055158 n has distinct digits in descending order and n=a+b where a has the digits of n in another order and b has the digits of n in ascending order (perhaps with leading zeros).

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A121969 Numbers k such that if you subtract k-reversed from k you get a natural number with the same digits as k.

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A121970 Numbers k such that if you subtract k from its reversal you get a positive number with the same digits as k.

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Mathematica

A331468 Lexicographically earliest sequence of distinct triples (A,B,C) such that A + B = C with A, B, C anagrams of each other and A < B.

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