A328933 For any negative number, add the digits (assigning the negative sign just to the first digit), square the result and add it to the original number. This sequence shows negative numbers which give a positive answer.

-2, -3, -4, -5, -6, -7, -8, -9, -15, -16, -17, -18, -19, -28, -29, -159, -168, -169, -178, -179, -187, -188, -189, -197, -198, -199

Offset: 1

Author

Andrew Toothill, Oct 31 2019

Keywords

• sign
• base
• dumb
• fini
• full

Comments

These numbers are the Zombie Numbers.

Start with any negative (dead) number, add the digits (attaching the negative to the first digit), square the result and add it to the original number. If your answer is positive then you have a 'zombie number' which has 'risen from the dead'.

The list is finite with 26 terms.

Negative integer k such that (digitsum(-k) - 2*(1st digit of -k))^2 > -k. - Stefano Spezia, Nov 01 2019

Examples

			-27 is not a zombie number because -2 + 7 = 5 and -27 + (5)^2 = -2.
-28 is a zombie number because -2 + 8 = 6 and -28 + (6)^2 = 8.
		

Links

• Ed Southall, Twitter post about Halloween maths, SolveMyMaths, Oct 31 2019.

Programs

Mathematica

-Select[Range[200],(Total[IntegerDigits[#]]-2*First[IntegerDigits[#]])^2-#>0&] (* Stefano Spezia, Nov 01 2019 *)

PARI

f(n) = my(d=digits(n), s = sumdigits(n) - 2*d[1]); s^2 + n;
isok(n) = f(n) > 0;
forstep(n=-1, -10000, -1, if (isok(n), print1(n, ", "))) \\ Michel Marcus, Oct 31 2019