A274580 Digital difference of n: the most significant decimal digit of n minus the sum of the other digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Felix Fröhlich, Jun 29 2016

Keywords

• sign
• easy
• base

Comments

If A007953(n) is seen as giving the resulting sum when inserting "+" signs between the digits of n, then a(n) gives the resulting difference when inserting "-" signs between the digits of n.

a(n) = 0 if and only if n is in A193772.

Signed version of A040997.

First differs from A225693 at n = 101.

abs(a(n)) first differs from abs(A055017(n)) at n = 102.

Examples

			a(13) = 1 - 3 = -2.
a(74) = 7 - 4 = 3.
a(211) = 2 - 1 - 1 = 0.
		

Crossrefs

Cf. A007953, A007954.

Programs

Mathematica

Table[Fold[#1 - #2 &, IntegerDigits@ n], {n, 76}] (* Michael De Vlieger, Jun 30 2016 *)
Table[-Differences[(Total/@TakeDrop[IntegerDigits[n],1])],{n,100}]//Flatten (* Harvey P. Dale, Dec 27 2022 *)

PARI

diffdigits(n) = my(d=digits(n), dd=d[1]); for(k=2, #d, dd=dd-d[k]); dd
a(n) = diffdigits(n)

Formula

a(n) = A000030(n) - A007953(A217657(n)).