A260861 Base-11 representation of a(n) is the concatenation of the base-11 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 144, 17689, 2143296, 259371025, 31384248336, 3797497946089, 459497294348544, 55599173087763361, 6727499948806851600, 8954302429379707945271, 131099941868210323821706774, 1919434248892467772593071038679, 28102436838034620750856132266604106

Offset

0,3

Comments

The first prime in this sequence is a(13) = A260871(9). Since a(11) is not prime, the base 11 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 = 11, 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) = (11+1)^2 = 11^2 + 2*11 + 1 = 121_11, concatenation of (1, 2, 1).
a(12) = 123456789a101110a987654321_11 is the concatenation of (1, 2, 3, ..., 9, a, 10, 11, 10, a, 9, ..., 1), where "a, 10, 11" are the base-11 representations of 10, 11, 12.

Prog

(PARI) a(n, b=11)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-11 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

Sequence in context: A238284 A249181 A352511 * A079658 A280024 A091037

Adjacent sequences: A260858 A260859 A260860 * A260862 A260863 A260864

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved