

A336324


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


2



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
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OFFSET

1,2


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.


LINKS

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


EXAMPLE

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.


CROSSREFS

Cf. A336325 (same idea, but between L and R we insert R^L instead of L^R), A335600 (poor sandwiches), A335854 (digitalroot sandwiches), A335886 (heavy sandwiches).
Sequence in context: A180700 A077526 A083764 * A335886 A141236 A079032
Adjacent sequences: A336321 A336322 A336323 * A336325 A336326 A336327


KEYWORD

base,nonn


AUTHOR

Carole Dubois and Eric Angelini, Jul 17 2020


STATUS

approved



