A251860 - OEIS

%I #16 May 26 2015 19:42:24

%S 254,64581,64582,64611,64612,64626,64676,64698,64706,64711,64712,

%T 64724,2159962,3232398,1998135468,11520892878,17788754556

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

%C 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:

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

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

%C a(18) > 8*10^10. - _Giovanni Resta_, May 26 2015

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

%e 254 = concat(2,54) and prime(2) + prime(54) = 3 + 251 = 254.

%e 64581 = concat(6458,1) and prime(6458) + prime(1) = 64579 + 2 = 64581.

%e 64582 = concat(6458,2) and prime(6458) + prime(2) = 64579 + 3 = 64582. Etc.

%p with(numtheory):P:=proc(q) local s,t,k,n;

%p 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

%p then print(n); break; fi; fi; od; od; end: P(10^6);

%p # program from _R. J. Mathar_, Jan 22 2015:

%p isA251860 := proc(n)

%p     local ti,i1,i2;

%p     if n >= 10 then

%p         for ti from 1 to A055642(n)-1 do

%p             i1 := modp(n,10^ti) ;

%p             i2 := floor(n/10^ti) ;

%p             if i1 > 0 and i2 > 0 then

%p                 if ithprime(i1)+ithprime(i2) = n then

%p                     return true;

%p                 end if;

%p             end if;

%p         end do:

%p         false;

%p     else

%p         false;

%p     end if;

%p end proc:

%p for n from 1 do

%p     if isA251860(n) then

%p         print(n);

%p     end if;

%p end do:

%o (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

%Y Cf. A000040, A249766.

%K nonn,base,more

%O 1,1

%A _Paolo P. Lava_, Dec 10 2014

%E a(13)-a(17) from _Giovanni Resta_, May 26 2015