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User: Andrew Toothill

Andrew Toothill has authored 2 sequences.

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

Andrew Toothill, Oct 31 2019

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

			-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.

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

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

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

A321676 a(1)=1; for n > 1, a(n) is a(n-1) plus the number of vowels in the name of a(n-1) in US English.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 14, 18, 22, 24, 27, 30, 31, 34, 37, 40, 41, 44, 47, 50, 51, 54, 57, 60, 61, 64, 67, 70, 72, 75, 79, 83, 87, 91, 95, 99, 103, 109, 115, 122, 128, 135, 142, 148, 155, 162, 168, 175, 183, 191, 199, 207, 212, 217, 224, 230, 234, 240, 244, 250

Offset: 1

Andrew Toothill, Dec 02 2018

This sequence takes into account the numbers written as words; for example, "fifty-seven" contains three vowels, so 3 is added to 57 to create the next term. The word "and" is not included in US English (cf. A158352), so 115 is written as "one hundred fifteen". This sequence is puzzling as it shares its first 6 terms with the odd numbers before jumping to 14, then 18. When only given the first 8 terms it can be very difficult to spot the rule.

Assumes "y" in e.g. "fifty" is not a vowel. - Chai Wah Wu, Dec 17 2018

Cf. A005589, A037196, A139282, A158352.

vowelCount[n_] := StringCount[IntegerName[n, "Words"], {"a","e","i","o","u"}]; f[n_] := n + vowelCount[n]; NestList[f, 1, 100] (* Amiram Eldar, Dec 10 2018 *)

from itertools import accumulate, repeat
from num2words import num2words
A321676_list = list(accumulate(repeat(1,100), lambda x, : x+sum(num2words(x).count(d) for d in 'aeiou'))) # _Chai Wah Wu, Dec 17 2018

a(n) = A139282(n) for n >= 2. - Chai Wah Wu, Dec 17 2018

More terms from Amiram Eldar, Dec 10 2018

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User: Andrew Toothill

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.

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A321676 a(1)=1; for n > 1, a(n) is a(n-1) plus the number of vowels in the name of a(n-1) in US English.

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