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A336325
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The power sandwiches sequence, version 2 (see Comments lines for definition).
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2
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1, 11, 111, 1111, 112, 6, 4, 66, 12, 9, 64, 440, 96, 666, 125, 129, 95, 3, 14, 41, 642, 5, 6400, 964, 665, 6666, 15, 51, 93, 8, 7, 420, 48, 99, 512, 53, 33, 142, 56, 411, 62, 32, 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
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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).
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.
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LINKS
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EXAMPLE
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The first successive sandwiches are: 111, 111, 111, 111, 2646, 612964,...
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.
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.
(...)
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.
The successive sandwiches rebuild, digit by digit, the starting sequence.
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CROSSREFS
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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).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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