A260866 Base-16 representation of a(n) is the concatenation of the base-16 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 289, 74529, 19088161, 4886709025, 1250999747361, 320255971115809, 81985529178309409, 20988295478809805601, 5373003642721911784225, 1375488932539155041567521, 352125166730061220638180129, 90144042682896272963324429089, 23076874926821455486290258903841

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=16, 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..14.

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

Formula

For n < b = 16, 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) = (16+1)^2 = 16^2 + 2*16 + 1 = 121_16, concatenation of (1, 2, 1).
a(17) = 123456789abcdef101110fedcba987654321_16 is the concatenation of (1, 2, 3, ..., 9, a, ..., f, 10, 11, 10, f, e, ..., 1), where the middle "10, 11, 10" are the base-16 representations of 16, 17, 16.

Prog

(PARI) a(n, b=16)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-16 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260865 for variants in other bases.

Sequence in context: A156161 A114762 A226747 * A252360 A125249 A013761

Adjacent sequences: A260863 A260864 A260865 * A260867 A260868 A260869

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved