A121969 -id:A121969 - cp's OEIS frontend

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

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

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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