A336324 The power sandwiches sequence, version 1 (see Comments lines for definition).

1, 2, 22, 4, 221, 6, 44, 16, 21, 66, 640, 9, 64, 41, 166, 42, 1666, 46, 65, 660, 19, 9100, 7, 76, 96, 642, 5, 641, 11, 6409, 6421, 1640, 964, 646, 656, 657, 77, 6601, 193, 8, 74, 20, 48, 990, 17, 78, 23, 54, 3, 765, 31, 441, 9646, 6566, 225, 55, 777, 661, 111, 669, 100, 776, 966, 1110, 194, 12, 9666

Offset: 1

Author

Carole Dubois and Eric Angelini, Jul 17 2020

Keywords

• base
• nonn

Comments

Imagine we would have a pair of adjacent integers in the sequence like [1951, 2020]. The sandwich would then be made of the rightmost digit R of a(n), the leftmost digit L of a(n+1) and, in between, L^R. The pair [1951, 2020] would then produce the power sandwich 122. Please note that the pair [2020, 1951] would produce the power and genuine sandwich 011 (we keep the leading zero: these are sandwiches after all, not integers).

Now we want the sequence to be the lexicographically earliest sequence of distinct positive terms such that the successive sandwiches emerging from the sequence rebuild it, digit after digit.

Examples

			The first successive sandwiches are: 122, 242, 2164, 4162, 166, 640964, ...
The first one (122) is visible between a(1) = 1 and a(2) = 2; we get the sandwich by inserting 2^1 = 2.
The second sandwich (242) is visible between a(2) = 2 and a(3) = 22; we get this sandwich by inserting 2^2 = 4 between 2 and 2.
The third sandwich (2164) is visible between a(3) = 22 and a(4) = 4; we get this sandwich by inserting 4^2 = 16 between 2 and 4; etc.
The successive sandwiches rebuild, digit by digit, the starting sequence.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..541

Crossrefs

Cf. A336325 (same idea, but between L and R we insert R^L instead of L^R), A335600 (poor sandwiches), A335854 (digital-root sandwiches), A335886 (heavy sandwiches).