

A260860


Base60 representation of a(n) is the concatenation of the base60 representations of 1, 2, ..., n, n1, ..., 1.


6



0, 1, 3721, 13402921, 48250954921, 173703464074921, 625332472251274921, 2251196900199483274921, 8104308840723833403274921, 29175511826606141868603274921, 105031842575782131223980603274921, 378114633272815673636150700603274921
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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 baseb sequence, as here with b=60, and c = R(b,b) = (b^b1)/(b1) is the baseb 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^n1)/(b1) are the baseb 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 base60 representations of 60, 61, 60.


PROG

(PARI) a(n, b=60)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base60 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



