A260865 Base-15 representation of a(n) is the concatenation of the base-15 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 256, 58081, 13075456, 2942086081, 661970995456, 148943498386081, 33512287502995456, 7540264693665886081, 1696559556157202995456, 381725900136606353386081, 85888327530754964702995456, 19324873694420145086040886081

Offset

0,3

Comments

See A260343 for the bases b such that B(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=15, and c = R(b,b) = (b^n-1)/(b-1) is the base-b repunit of length b.

Links

Table of n, a(n) for n=0..13.

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

Formula

For n < b = 15, 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.

Example

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = (15+1)^2 = 15^2 + 2*15 + 1 = 121_15, concatenation of (1, 2, 1).
a(16) = 123456789abcde101110edcba987654321_15 is the concatenation of (1, 2, 3, ..., 9, a, ..., e, 10, 11, 10, e, d, ..., 1), where "e, 10, 11" are the base-15 representations of 14, 15, 16.

Prog

(PARI) a(n, b=15)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-15 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

Sequence in context: A237068 A204302 A264096 * A205173 A205416 A229103

Adjacent sequences: A260862 A260863 A260864 * A260866 A260867 A260868

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved