OFFSET
1,1
COMMENTS
From Robert Israel, Nov 27 2024: (Start)
If 10^d + 1 has a prime factor p such that 53 is not a square mod p, then there are no terms k where k + 7 has d digits.
For example, there are no terms where d == 2 (mod 4), since in that case 10^d + 1 is divisible by 101, and 53 is not a square mod 101. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..85 (all terms with up to 113 digits).
EXAMPLE
72757727//72757734 = 85298138 * 85298143, where // denotes concatenation.
MAPLE
f:= proc(d) # terms where k+7 has d digits
local S, x, R, k;
S:= map(t -> rhs(op(t)), [msolve(x*(x+5) = 7, 10^d+1)]);
R:= NULL:
for x in S do
k := (x*(x+5)-7)/(10^d+1);
if ilog10(k+7) = d - 1 then R:= R, k fi
od:
op(sort([R]))
end proc:
map(f, [$1..31]); # Robert Israel, Nov 27 2024
CROSSREFS
KEYWORD
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved