A249766 -id:A249766 - cp's OEIS frontend

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

Paolo P. Lava, Dec 10 2014

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

			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.

Cf. A000040, A249766.

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:

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

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

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

A258319 Numbers n such that n = concat(a,b) and n = phi(n) + phi(a) + phi(b), with a>0 and b>0, where phi(n) is the Euler totient function of n.

Original entry on oeis.org

25, 177, 1177, 2501, 17105, 21337, 22681, 32581, 217009, 409501, 561601, 577501, 861841, 1025821, 1401841, 1738081, 2836465, 8331361, 10284193, 19971901, 20103001, 27835921, 31949921, 34897501, 100763053, 107314217, 111512701, 121806001, 150658561, 155874001

Offset: 1

Paolo P. Lava, May 26 2015

			25 = concat(2,5); phi(25) + phi(2) + phi(5) = 20 + 1 + 4 = 25;
177 = concat(1,77); phi(177) + phi(1) + phi(77) = 116 + 1 + 60 = 177; etc.

Giovanni Resta, Table of n, a(n) for n = 1..50

Cf. A000010, A239562, A249766, A251605, A251860, A253824, A253825, A255725, A255726, A257897.

with(numtheory); P:=proc(q) local a, b, i; global n; for n from 1 to q do
for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
if a>0 and b>0 then if phi(n)+phi(a)+phi(b)=n
then print(n); break; fi; fi; od; od; end: P(10^9);

a(18) inserted by Giovanni Resta, May 27 2015

cp's OEIS Frontend

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

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