A380202 Number of card moves to deal n cards using the SpellUnder-Down dealing.

4, 8, 14, 19, 24, 28, 34, 40, 45, 49, 56, 63, 72, 81, 89, 97, 107, 116, 125, 136, 146, 156, 168, 179, 190, 200, 212, 224, 235, 246, 256, 266, 278, 289, 300, 310, 322, 334, 345, 355, 364, 373, 384, 394, 404, 413, 424, 435, 445, 455, 464, 473, 484, 494, 504, 513, 524, 535, 545, 555, 564, 573, 584, 594, 604, 613, 624, 635, 645

Offset: 1

Author

Tanya Khovanova and the MIT PRIMES STEP junior group, Jan 16 2025

Keywords

• nonn
• word

Comments

In SpellUnder-Down dealing, we spell the number of the next card, putting a card under for each letter in the number, then we deal the next card. So we start with putting 3 cards under, for O-N-E, then deal, then 3 under for T-W-O, then deal, then 5 under for T-H-R-E-E, then deal. The dealing sequence is highly irregular because it depends on English spelling. The dealing pattern starts: UUUDUUUDUUUUUD.

Examples

			The dealing pattern to deal three cards is UUUDUUUDUUUUUD. It contains 14 letters, thus, a(3) = 14.
		

Crossrefs

Cf. A005589, A006257, A067278, A225381, A321298, A378635, A380201, A380204, A380246, A380247, A380248.

Formula

a(n) = A067278(n) + n.