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A328933
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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.
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0
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-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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=1..26.
Ed Southall, Twitter post about Halloween maths, SolveMyMaths, Oct 31 2019.
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EXAMPLE
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-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.
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MATHEMATICA
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-Select[Range[200], (Total[IntegerDigits[#]]-2*First[IntegerDigits[#]])^2-#>0&] (* Stefano Spezia, Nov 01 2019 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A032992 A190298 A069118 * A032978 A197181 A260352
Adjacent sequences: A328930 A328931 A328932 * A328934 A328935 A328936
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KEYWORD
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sign,base,dumb,fini,full
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AUTHOR
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Andrew Toothill, Oct 31 2019
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STATUS
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approved
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