A336895 The prime sandwiches sequence (see Comments lines for definition).

1, 22, 2, 3, 225, 33, 7, 25, 11, 331, 37, 71, 72, 5, 19, 112, 3312, 9, 373, 17, 13, 77, 24, 15, 54, 31, 94, 712, 53, 32, 59, 99, 6, 133, 67, 177, 113, 73, 777, 92, 4, 8, 315, 89, 549, 731, 10, 194, 103, 7210, 75, 310, 93, 21, 135, 91, 27, 991, 316, 61, 371, 313, 96, 714, 917, 151, 131, 57

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 of a(n), the leftmost digit of a(n+1) and, in between, the smallest prime p not yet inserted in a sandwich. The pair [1951, 2020] would then produce the sandwich 1p2. Please note that the pair [2020, 1951] would produce the genuine sandwich 0p1 (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..1964

Example

The first successive sandwiches are: 122, 232, 253, 372, 5113, 3137,...
The 1st one (122) is visible between a(1) = 1 and a(2) = 22 (insert 2).
The 2nd one (232) is visible between a(2) = 22 and a(3) = 2 (insert 3).
The 3rd one (253) is visible between a(3) = 2 and a(4) = 3 (insert 5).
The 4th one (372) is visible between a(4) = 3 and a(5) = 225 (insert 7).
The 5th one (5113) is visible between a(5) = 225 and a(6) = 33 (insert 11); etc.
The successive sandwiches rebuild, digit by digit, the starting sequence.

Crossrefs

Cf. A336894 (empty sandwiches), A335600 (poor sandwiches).

Sequence in context: A040476 A040480 A040479 * A040481 A058288 A040482

Adjacent sequences: A336892 A336893 A336894 * A336896 A336897 A336898

Keyword

base,nonn

Author

Carole Dubois and Eric Angelini, Aug 07 2020

Status

approved