[seqfan] Re: Divisors of the concatenation of n+1 and n
Vladimir Shevelev
shevelev at bgu.ac.il
Wed Jun 3 13:33:39 CEST 2015
In May I submitted also the following sequence A258080:
Smallest nonnegative residue of sum of concatenations of n+1,n and n,n+1 modulo n*(n+1).
1, 1, 5, 19, 1, 17, 53, 43, 29, 31, 79, 29, 179, 199, 11, 69, 169, 317, 139, 361, 185, 497, 331, 149, 601, 439, 263, 73, 739, 581, 411, 229, 35, 1019, 871, 713, 545, 367, 179, 1621, 1495, 1361, 1219, 1069, 911, 745, 571, 389, 199, 1, 2447, 2337, 2221, 2099
containing rather many primes. I even asked Peter: How many terms from the first 2000 of A258080, by your b-file, contains 0,1,2,3,... distinct prime divisors?
By the first 54 terms we have 4 0's, 37 1's, 11 2's and 2 3's. Does such asymmetry continue? Instead 2000, Peter considered the first 2,000,000 terms and obtained
{8,225795,618065,662000,364888,110244,17764,1204,32} with only 11.3% of 1's
(although instead of approx. 7.4% numbers with one prime divisor in interval [2, 2,000,000]).
Best regards,
Vladimir
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Eric Angelini [Eric.Angelini at kntv.be]
Sent: 03 June 2015 12:48
To: Sequence Fanatics Discussion list
Subject: [seqfan] Divisors of the concatenation of n+1 and n
Hello SeqFans,
t(n) is the smallest unused integer so far in T such that t(n) is a divisor of the concatenation of n+1 and n.
n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
concat = 21 32 43 54 65 76 87 98 109 1110 1211 1312 1413 1514 1615 1716 1817 1918 2019 2120 2221 2322
T = 1, 2 43, 3, 5, 4,29, 7,109, 6, 173, 8, 9, 757, 17, 11, 23, 14, 673, 10, 2221, 18,...
Example:
The divisors of 1413 (concatenation of 14 and 13) are 1, 3, 9, 157, 471 and 1413. As 1 and 3 appear already in T, we have t(13) = 9.
Is T a permutation of the integers > 0 ?
Best,
É.
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