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A336325 The power sandwiches sequence, version 2 (see Comments lines for definition). 2
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 (list; graph; refs; listen; history; text; internal format)
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, 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.

LINKS

Carole Dubois, Table of n, a(n) for n = 1..1192

EXAMPLE

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.

CROSSREFS

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).

Sequence in context: A110444 A265380 A114397 * A098595 A273978 A334131

Adjacent sequences:  A336322 A336323 A336324 * A336326 A336327 A336328

KEYWORD

base,nonn

AUTHOR

Carole Dubois and Eric Angelini, Jul 17 2020

STATUS

approved

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Last modified October 19 15:34 EDT 2021. Contains 348091 sequences. (Running on oeis4.)