A251860 Numbers n = concat(s,t) such that n = prime(s) + prime(t).

254, 64581, 64582, 64611, 64612, 64626, 64676, 64698, 64706, 64711, 64712, 64724, 2159962, 3232398, 1998135468, 11520892878, 17788754556

Offset: 1

Author

Paolo P. Lava, Dec 10 2014

Keywords

• nonn
• base
• more

Comments

If we consider the product instead of the sum, n = concat(s,t) = prime(s) * prime(t), then the first terms are 14 and 2127. In fact:

14 = concat(1,4) and prime(1) * prime(4) = 2 * 7 = 14.

2127 = concat(2,127) and prime(2) * prime(127) = 3 * 709 = 2127.

a(18) > 8*10^10. - Giovanni Resta, May 26 2015

Examples

			254 = concat(2,54) and prime(2) + prime(54) = 3 + 251 = 254.
64581 = concat(6458,1) and prime(6458) + prime(1) = 64579 + 2 = 64581.
64582 = concat(6458,2) and prime(6458) + prime(2) = 64579 + 3 = 64582. Etc.
		

Crossrefs

Cf. A000040, A249766.

Programs

Maple

with(numtheory):P:=proc(q) local s,t,k,n;
for n from 1 to q do for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k); if s*t>0 then if ithprime(s)+ithprime(t)=n
then print(n); break; fi; fi; od; od; end: P(10^6);
# program from R. J. Mathar, Jan 22 2015:
isA251860 := proc(n)
    local ti,i1,i2;
    if n >= 10 then
        for ti from 1 to A055642(n)-1 do
            i1 := modp(n,10^ti) ;
            i2 := floor(n/10^ti) ;
            if i1 > 0 and i2 > 0 then
                if ithprime(i1)+ithprime(i2) = n then
                    return true;
                end if;
            end if;
        end do:
        false;
    else
        false;
    end if;
end proc:
for n from 1 do
    if isA251860(n) then
        print(n);
    end if;
end do:

PARI

isok(n) = {my(nb = #Str(n)); for (k=1, nb-1, s = n\10^k; t = n % 10^k; if (s && t && prime(s)+ prime(t) == n, return (1));); return (0);} \\ Michel Marcus, Dec 10 2014

Formula

n = concat(s,t) = A000040(s) + A000040(t).

Extensions

a(13)-a(17) from Giovanni Resta, May 26 2015