OFFSET
0,3
COMMENTS
Efficient means the smallest possible a(n), cf. example. From n = 9*9+8*4+3 = 116 on, the terms (coded in base 10) become ambiguous because digits may be larger than 9, e.g., 1000 could mean 1*16 or 10*9. One possible convention to avoid ambiguity would be to reserve as many digits as might be required for the largest possible coefficient: 2 digits for the coefficients of 9 (which may reach 16-1 = 15) through 81; 3 digits for the coefficients of 100 through 30^2, 4 digits for the coefficients of 31^2 (which may reach 32^2-1 = 1023) etc. - M. F. Hasler, Jul 25 2015
REFERENCES
F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.
LINKS
EXAMPLE
a(50)=280 since 2*9+8*4+0*1=50; writing 20000 for 2*25 or 3xyz (for 3*16+x*9+y*4+z) or 5yz or 4yz or 3yz would be less efficient (larger "result" when read in base 10), and it is not possible to write 50 as 1*9+y*4+z*1 with y<9 and z<4.
PROG
(PARI) a(n, s=0)={v=[3]; until(v[#v]>=n, v=concat(v, v[#v]+((2+#v)^2-1)*(1+#v)^2)); for(i=1, #v-1, s=s*10+t=max(ceil((n-v[#v-i])/(#v-i+1)^2), 0); n-=t*(#v-i+1)^2); s*10+n} \\ M. F. Hasler, Jul 25 2015
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Jun 07 2000
EXTENSIONS
Corrected and edited by M. F. Hasler, Jul 25 2015
STATUS
approved