A260860 Base-60 representation of a(n) is the concatenation of the base-60 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 3721, 13402921, 48250954921, 173703464074921, 625332472251274921, 2251196900199483274921, 8104308840723833403274921, 29175511826606141868603274921, 105031842575782131223980603274921, 378114633272815673636150700603274921

Offset

0,3

Comments

See A260343 for the bases b such that A260851(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=60, and c = R(b,b) = (b^b-1)/(b-1) is the base-b repunit of length b.

Links

Table of n, a(n) for n=0..11.

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

Formula

For n < b = 60, 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) = (60+1)^2 = 60^2 + 2*60 + 1 = 121_60, concatenation of (1, 2, 1).
a(61) = 123...101110...21_60, which is the concatenation of (1, 2, 3, ..., 10, 11, 10, ..., 2, 1), where the middle "10, 11, 10" are the base-60 representations of 60, 61, 60.

Prog

(PARI) a(n, b=60)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-60 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

Sequence in context: A296908 A237736 A289512 * A221013 A224436 A031559

Adjacent sequences: A260857 A260858 A260859 * A260861 A260862 A260863

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved