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
KEYWORD
base,nonn
AUTHOR
Carole Dubois and Eric Angelini, Jul 17 2020
STATUS
approved