A260857 Base-7 representation of a(n) is the concatenation of the base-7 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 64, 3249, 160000, 7845601, 384473664, 131870760799, 316621469105950, 760208147660763999, 1825259762561514314050, 4382448689911580334132199, 10522259304477772232578647150, 25263944590051134455098854865399, 60658730960712773989601560650105250

Offset

0,3

Comments

Base-7 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

The base 7 is not listed in A260343, because a(7) = A260851(7) = 131870760799 = 12345610654321_7 is not prime and therefore not in A260852. See these sequences for more information.

Links

Table of n, a(n) for n=0..14.

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

Example

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 64 = (7+1)^2 = 7^2 + 2*7 + 1 = 121_7 is the concatenation of (1, 2, 1).
a(8) = 316621469105950 = 123456101110654321_7 is the concatenation of (1, 2, 3, 4, 5, 6, 10, 11, 10, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-7 representations of 7, 8, 7.

Mathematica

Table[FromDigits[Flatten[Join[IntegerDigits[Range[n], 7], IntegerDigits[ Range[ n-1, 1, -1], 7]]], 7], {n, 0, 20}] (* Harvey P. Dale, Nov 02 2017 *)

Prog

(PARI) a(n, b=7)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Sequence in context: A342709 A264094 A181249 * A183814 A281343 A298286

Adjacent sequences: A260854 A260855 A260856 * A260858 A260859 A260860

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved