A206770 Smallest number k such that sigma(k-2*n)=sigma(k)-2*n.

5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 21, 31, 37, 37, 37, 41, 28, 33, 47, 47, 53, 53, 53, 59, 59, 44, 61, 67, 67, 67, 71, 57, 73, 79, 79, 79, 83, 83, 69, 89, 74, 101, 68, 97, 97, 85, 101, 103, 107, 107, 109, 113, 93, 131, 127, 127, 131, 127, 127, 127

Offset: 1

Author

Paolo P. Lava, Jan 10 2013

Keywords

• nonn

Comments

Note all k>=1 are considered, even if k-2n<0. If the search space is k>=2n, variants of A020484 and A060264 appear. - R. J. Mathar, Jan 12 2013

Examples

			a(15)=37 because 37 is the minimum number for which sigma(37-2*15)=sigma(7)=8 and sigma(37)-2*15=38-30=8.
		

Crossrefs

Cf. A054906

Programs

Maple

A206770:=proc(q)
local k,n;
for n from 1 to q do
for k from 1 to q do
  if sigma(k-2*n)=sigma(k)-2*n then print(k); break; fi;
od; od; end:
A206770(1000000000);
A206770 := proc(n)
    local k ;
    for k from 1 do
        if numtheory[sigma](k-2*n) = numtheory[sigma](k)-2*n then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Jan 12 2013