A323143 Lexicographically earliest infinite sequence of envelope numbers that are inserted into the largest possible envelopes (see the Comments and the Crossrefs sections).

0, 902, 29022, 4290222, 342902224, 13429022244, 6134290222446, 161342902224468, 31613429022244686, 5316134290222446864, 753161342902224468642, 17531613429022244686428, 6175316134290222446864283, 561753161342902224468642837, 35617531613429022244686428373, 8356175316134290222446864283739

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jan 10 2019

Keywords

• base
• nonn

Comments

Every term is equal to the term after it, except for the first and the last digit; those two digits, concatenated in that order, constitute the envelope; a(n) is always a multiple of a(n+1)'s envelope, this envelope being the largest possible so that the sequence doesn't stop.

Examples

			The first term > 0 is 902, and we see that 902 is indeed an envelope number as 0 is a multiple of 92; as we want always to insert an envelope number into the biggest next possible envelope, we try first 909, but 909 has no 2-digit divisor; nor could we select 908 (for the same reason), nor 907 (as 907 is prime), nor 906 (as 906 too has no 2-digit divisor), nor 905 or 904 (for the same reason), nor 903 (as 903 would produce the envelope number 29031 which has itself no 2-digit divisor); 902 is ok as 902 has two 2-digit divisors, 11 and 22: we thus keep the biggest one (22) to build a(3) = 29022; a(3) has itself three 2-digit divisors, 14, 21 and 42: we keep the biggest one to build a(4) = 4290222; this number has 16 divisors altogether, but three of them are 2-digit numbers, 17, 34 and 51; we will keep 34 (as 51 cannot produce an infinite sequence) to build a(5) = 342902224, etc.
A way to spare some space in presenting this sequence, would be to align, after a(1) = 0, the successive divisors that are kept; this would form the sequence 0,92,22,42,34,14,66,18,36,54,72,18,63,57,33,89,47,11,21,43,59,47,79,67,61,43,27,27,99,81,19,17,63,27,99,27,27,93,71,59,11,49,11,69,87,39,79,79,91,33,39,43,53,43,11,93,27,51,57,81,81,97,29,99,91,37,37,21,33,69,63,33,39,23,61,51,27,33,23,73,11,67,99,27,27,69,...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..135

Crossrefs

Cf. A323142 (the definition of an envelope number and the first simple ones).