login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335854 The digital-root sandwiches sequence (see Comments lines for definition). 3
11, 9, 99, 999, 9999, 9990, 1, 112, 12, 3, 125, 33, 4, 15, 8, 337, 44, 5, 154, 88, 2, 37, 24, 49, 55, 6, 14, 38, 81, 22, 53, 7, 92, 48, 495, 552, 66, 71, 47, 387, 813, 227, 531, 77, 79, 26, 483, 45, 152, 86, 64, 715, 471, 376, 83, 52, 73, 51, 87, 75, 792, 261, 43, 74, 56, 121, 863, 642, 759, 41, 436, 58, 385, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Imagine we would have a pair of adjacent integers in the sequence like [1951, 2020]. A digital-root sandwich would then be made of the rightmost digit of a(n), the leftmost digit of a(n+1) and, in between, the digital root of their sum. The pair [1951, 2020] would then produce the DR-sandwich 132. Please note that the pair [2020, 1951] would produce the genuine DR-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..428

EXAMPLE

The first successive sandwiches are: 119, 999, 999, 999, 999, 011, 121, 231, ...

The first one (119) is visible between a(1) = 11 and a(2) = 9; we get the sandwich by inserting the digital root of the sum 1 + 9 = 10 (which is 1) between 1 and 9.

The second sandwich (999) is visible between a(2) = 9 and a(3) = 99; we get the sandwich by inserting the digital root of the sum 9 + 9 = 18 (which is 9) between 9 and 9.

The third sandwich (999) is visible between a(3) = 99 and a(3) = 999; we get the sandwich by inserting the digital root of the sum 9 + 9 = 18 (which is 9) between 9 and 9.

(...)

The sixth sandwich (011) is visible between a(6) = 9990 and a(7) = 1; we get the sandwich by inserting the digital root of the sum 0 + 1 = 1 (which is 1) between 0 and 1; etc.

The successive sandwiches rebuild, digit after digit, the starting sequence.

CROSSREFS

Cf. A335600 (first definition of such a sandwich) and A010888 (digital root of n).

Sequence in context: A072208 A210284 A219746 * A220664 A038323 A121154

Adjacent sequences:  A335851 A335852 A335853 * A335855 A335856 A335858

KEYWORD

base,nonn

AUTHOR

Carole Dubois and Eric Angelini, Jun 26 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 29 18:27 EDT 2020. Contains 337432 sequences. (Running on oeis4.)