[seqfan] Re: Divisors of the concatenation of n+1 and n

[Vladimir Shevelev]

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 primes
instead of approx. 6% primes <=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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