In the mean time I'll just make my move, since it's unaffected by menno's and to keep the game moving:
[5, 9, 10, 27, 48, 66, 98] {
n2 + k, -3 < k < 3
} numbers that are within two of a perfect square
(4, 9, 9, 25, 49, 64, 100 are the close squares)
Note that each of the 10 squares 12 through 102 contributes at most 5 numbers to this set between 1 and 100, and there is some overlap, so it contains fewer than 50 of the numbers between 1 and 100.
Great. I don't want to do too much reinterpreting of sequences, and the original player has the final say on what the rules for the sequence are. Please speak up if I misinterpret your rules. I think it is okay to work together to make the starting move a sequence be valid or make the closed form be error free.
It would have been better if I pointed out the problem with the six initially and offered to let McMenno come up with a change himself. I'll try to do that in the future, because I think I did overstep here. Sorry about that.
Finished:
{
n2 ± [0, 2]
} numbers within 2 of a perfect square
McMenno has:
[14, 35, 343] {
7n
} divisible by 7
[5, 6, 100] numbers used in 0, including substrings of other numbers, but not including the deck spoiler
Implosion has 7 points and:
[15, 53, 91] {
n = a010d + a110d-1 + ... + ad100 with ai ≡ 1 (mod 2) ∀ i ∈ [1, 9], ∀ d > 0
} numbers with at least two digits, all of which are odd
DeathRowKitty has:
[8, 18, 34] n is the sum of the Scrabble point values of the letters in the US spelling of the numbers in the deck.
Consider a standard 52 card deck that starts in Ace - King, Ace - King, Ace - King, Ace - King order. Number the cards 1-52 in order with the first ace as 1 and the final king as 52. Suppose you perform an infinite sequence of perfect out-shuffles on this deck, each time renumbering the cards in the deck according to their new order. My sequence is those numbers that do not differ by a multiple of 52 from any number that ever indexes a non-face card (face cards are jack, queen, and king) that is 1 greater than a multiple of 4. So basically no ace, 5, or 9 can ever be numbered with a number in the sequence or any number ≡ mod 52 to any number in the sequence.
Every card ever numbered 38 is a 3, 6, 8, 10, J, or Q
Every card ever numbered 32 (84) is also a 3, 6, 8, 10, J, or Q
Every card ever numbered 30 (82) is a 2, 3, 4, 6, 8, or J
"NMSA called out all three of us as scum or null in his reads list. Good thing no one's actually reading that." -Enter
"NMSA was at least a pretty easy mislynch that I didn't have to get my hands dirty to attain" -RC