OFFSET
1,1
COMMENTS
Conjecture: The sequence only has 112 terms as listed in the b-file.
We have verified that there is no new term below 2*10^9.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..112
Zhi-Wei Sun, Mixed sums of primes and other terms, in: D. Chudnovsky and G. Chudnovsky (eds.), Additive Number Theory, Springer, New York, 2010, pp. 341-353.
Zhi-Wei Sun, Conjectures on representations involving primes, in: M. Nathanson (ed.), Combinatorial and Additive Number Theory II, Springer Proc. in Math. & Stat., Vol. 220, Springer, Cham, 2017, pp. 279-310. (See also arXiv:1211.1588 [math.NT], 2012-2017.)
EXAMPLE
a(9) = 13 since 13 - (4^1 - 1) = 2*5 is squarefree, 13 - (4^0 - 0) = 2^2*3 is not squarefree, and 13 - (4^k -k ) < 0 for any integer k > 1.
MATHEMATICA
f[n_]:=f[n]=4^n-n;
tab={}; Do[r=0; k=0; Label[bb]; If[f[k]>=m, Goto[aa]]; If[SquareFreeQ[m-f[k]], r=r+1]; If[r>1, Goto[cc]]; k=k+1; Goto[bb]; Label[aa]; If[r==1, tab=Append[tab, m]]; Label[cc], {m, 1, 640}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 17 2018
STATUS
approved