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 A173426 a(n) is obtained by starting with 1, sequentially concatenating all decimal numbers up to n, and then, starting from (n-1), sequentially concatenating all decimal numbers down to 1. 31
 1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 12345678910987654321, 123456789101110987654321, 1234567891011121110987654321, 12345678910111213121110987654321, 123456789101112131413121110987654321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first prime in this sequence is the 20-digit number a(10) = 12345678910987654321. On Jul 20 2015, Shyam Sunder Gupta reported on the Number Theory Mailing List that he has found what is probably the second prime in the sequence. This is the 2446th term, namely the 17350-digit probable prime 1234567..244524462445..7654321. - N. J. A. Sloane, Jul 29 2015 - Aug 03 2015 There are no other (PR)prime members in this sequence for n<60000. - Serge Batalov, Jul 29 2015 David Broadhurst gives heuristic arguments which suggest that this sequence contains infinitely many primes. See A075023 and A075024 for the smallest and largest prime factor of the terms. - M. F. Hasler, Jul 29 2015 Using summation in decimal length clades, one can obtain analytical expressions for the sequence: a(n) = A002275(n)^2, for 1 <= n < 10; a(n) = (120999998998*10^(4*n-28) - 2*10^(2*n-9) + 8790000000121)/99^2, for 10 <= n < 10^2; a(n) = (120999998998*10^(6*n-227) - (1099022*10^(6*n-406) + 242*10^(3*n-108) - 1087789*10^191)/111^2 + 8790000000121)/99^2, for 10^2 <= n < 10^3; etc. - Serge Batalov, Jul 29 2015 REFERENCES D. Broadhurst, Primes from concatenation: results and heuristics, Number Theory List, Aug 01 2015 and later postings. LINKS G. C. Greubel, Table of n, a(n) for n = 1..150 Shyam Sunder Gupta, Puzzle 794, Prime Puzzles Web Site. S. S. Gupta, A new 17350 digit Symmetric Prime, NmbrThry List, July 20, 2015 FORMULA a(n) = concatenate(1,2,3,...,n-2,n-1,n,n-1,n-2,...,3,2,1). MATHEMATICA Table[FromDigits[Flatten[IntegerDigits/@Join[Range[n], Reverse[Range[ n-1]]]]], {n, 15}] (* Harvey P. Dale, Sep 02 2015 *) PROG (PARI) A173426(n)=eval(concat(vector(n*2-1, k, if(k

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Last modified October 22 12:27 EDT 2019. Contains 328318 sequences. (Running on oeis4.)