A260862 Base-12 representation of a(n) is the concatenation of the base-12 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 169, 24649, 3553225, 511709641, 73686731209, 10610895808969, 1527969074670025, 220027547690625481, 31683966878707771849, 4562491230669011577289, 7883984846509322664831433, 163482309777203435651765004745, 3389969175540090458609916107975113

Offset

0,3

Comments

The first prime in this sequence is a(16) = A260871(11). Since a(12) is not prime, the base 12 is not listed in A260343.

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 = 12, we have a(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) = (12+1)^2 = 12^2 + 2*12 + 1 = 121_12, concatenation of (1, 2, 1).
a(13) = 123456789ab101110ba987654321_12 is the concatenation of (1, 2, 3, ..., 9, a, b, 10, 11, 10, b, ..., 1), where "b, 10, 11" are the base-12 representations of 11, 12, 13.

Prog

(PARI) a(n, b=12)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-12 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

Sequence in context: A264222 A051477 A227692 * A006051 A069742 A069743

Adjacent sequences: A260859 A260860 A260861 * A260863 A260864 A260865

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved