A260853 -id:A260853 - cp's OEIS frontend

A260863 Base-13 representation of a(n) is the concatenation of the base-13 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 196, 33489, 5664400, 957345481, 161792190756, 27342890695849, 4620948663553600, 780940325907974961, 131978915101424183716, 22304436652439380447009, 3769449794266138309731600, 8281481197999449959084458465, 236527384496061684935031509169004

Offset: 0

M. F. Hasler, Aug 01 2015

See A260343 for the bases b such that A260851(b) = A_b(b) = b*c + (c - b)*(1 + b*c), is prime, where A_b is the base-b sequence, as here with b = 13, and c = R(b,b) = (b^n-1)/(b-1) is the base-b repunit of length b.

			a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = (13+1)^2 = 13^2 + 2*13 + 1 = 121_13, concatenation of (1, 2, 1).
a(14) = 123456789abc101110cba987654321_13 is the concatenation of (1, 2, 3, ..., 9, a, b, c, 10, 11, 10, c, ..., 1), where "c, 10, 11" are the base-13 representations of 12, 13, 14.

D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015

Base-13 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

a(n,b=13)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))

For n < b = 13, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n-1)/(b-1) are the base-b repunits.

cp's OEIS Frontend

A260863 Base-13 representation of a(n) is the concatenation of the base-13 representations of 1, 2, ..., n, n-1, ..., 1.

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