cp's OEIS Frontend

A336325 The power sandwiches sequence, version 2 (see Comments lines for definition).

%I A336325 #11 Aug 06 2020 13:17:38
%S A336325 1,11,111,1111,112,6,4,66,12,9,64,440,96,666,125,129,95,3,14,41,642,5,
%T A336325 6400,964,665,6666,15,51,93,8,7,420,48,99,512,53,33,142,56,411,62,32,
%U A336325 55,156,2,5600,94,40,966,515,625,6661,531,25,511,936,561,88,20,97,152,77,240,1400,481,34,21,772,89,9590
%N A336325 The power sandwiches sequence, version 2 (see Comments lines for definition).
%C A336325 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, R^L. The pair [1951, 2020] would then produce the power sandwich 112. Please note that the pair [2020, 1951] would produce the power and genuine sandwich 001 (we keep the leading zeros: these are sandwiches after all, not integers).
%C A336325 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.
%H A336325 Carole Dubois, <a href="/A336325/b336325.txt">Table of n, a(n) for n = 1..1192</a>
%e A336325 The first successive sandwiches are: 111, 111, 111, 111, 2646, 612964,...
%e A336325 The first one (111) is visible between a(1) = 1 and a(2) = 11; we get the sandwich by inserting 1^1 = 1 between 1 and 1.
%e A336325 The second sandwich (111) is visible between a(2) = 11 and a(3) = 111; we get this sandwich by inserting 1^1 = 1 again between 1 and 1.
%e A336325 (...)
%e A336325 The fifth sandwich (2646) is visible between a(5) = 112 and a(6) = 6; we get this sandwich by inserting 2^6 = 64 between 2 and 6; etc.
%e A336325 The successive sandwiches rebuild, digit by digit, the starting sequence.
%Y A336325 Cf. A336324 (same idea, but between L and R we insert L^R instead of R^L), A335600 (poor sandwiches), A335854 (digital-root sandwiches), A335886 (heavy sandwiches).
%K A336325 base,nonn
%O A336325 1,2
%A A336325 _Carole Dubois_ and _Eric Angelini_, Jul 17 2020