%I #12 Apr 11 2022 22:19:32

%S 7,10,13,15,17,18,22,24,26,27,31,33,35,36,44,45,54,55,57,59,60,62,63,

%T 64,66,68,69,71,72,73,75,77,78,81,82,84,86,87,80,91,93,95,96,97,99,

%U 100,10,10,108,2,27,3,133,35,1337,39,0,15,153,1555,57,59,0,17773,75,77,178,179,180,188,18,1887,90

%N What remains from the sequence of positive integers (A000027) when all prime sums of two successive digits are erased.

%C After an erasure, we start reading again what is left, from the beginning, in order to spot the next pair of successive digits that will be erased. Those two digits can span a comma or a void.

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/03/effacer-les-paires-de-chiffres-somme.html">La Poussette</a>, personal blog (in French), April 2022.

%e We start with 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...

%e as 1 + 2 = 3 (prime) we erase those two digits; we are left with:

%e 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...

%e as 3 + 4 = 7 (prime) we erase those two digits; we are left with:

%e 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...

%e as 5 + 6 = 11 (prime) we erase those two digits; we are left with:

%e 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...

%e as 8 + 9 = 17 (prime) we erase those two digits; we are left with:

%e 7, 10, 11, 12, 13, 14, 15, 16, 17, ...

%e as 1 + 1 = 2 (prime) we erase those two digits; we are left with:

%e 7, 10, 12, 13, 14, 15, 16, 17, ...

%e as 1 + 2 = 3 (prime) we erase those two digits; we are left with:

%e 7, 10, 13, 14, 15, 16, 17, ...

%e as 1 + 4 = 5 (prime) we erase those two digits; we are left with:

%e 7, 10, 13, 15, 16, 17, ...

%e as 1 + 6 = 7 (prime) we erase those two digits; we are left with:

%e 7, 10, 13, 15, 17, ... etc.

%e What remains is this sequence.

%Y Cf. A000027, A000040.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Carole Dubois_, Apr 11 2022