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A323143 Lexicographically earliest infinite sequence of envelope numbers that are inserted into the largest possible envelopes (see the Comments and the Crossrefs sections). 2
0, 902, 29022, 4290222, 342902224, 13429022244, 6134290222446, 161342902224468, 31613429022244686, 5316134290222446864, 753161342902224468642, 17531613429022244686428, 6175316134290222446864283, 561753161342902224468642837, 35617531613429022244686428373, 8356175316134290222446864283739 (list; graph; refs; listen; history; text; internal format)
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.
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,...
Cf. A323142 (the definition of an envelope number and the first simple ones).
Sequence in context: A345789 A031528 A158406 * A284744 A111042 A115496

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Last modified September 29 12:57 EDT 2023. Contains 365771 sequences. (Running on oeis4.)