A281021 Primes k with (say) j digits that produce two other primes, x and y, from the sums x = Sum_{i=1..j} (k mod 10^i) and y = Sum_{i=0..j-1} (floor(k/10^i)).

2, 3, 5, 7, 137, 191, 379, 421, 683, 757, 919, 1001933, 1005553, 1006091, 1012463, 1012513, 1013431, 1013813, 1013921, 1013923, 1016027, 1016401, 1016681, 1019657, 1022729, 1022837, 1025537, 1028011, 1028569, 1030069, 1030889, 1030933, 1034069, 1038119, 1040057

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Paolo P. Lava, First 1000 primes with corresponding x and y

Example

k = 137 and x = 7 + 37 + 137 = 181, y = 137 + 13 + 1 = 151, both primes.

Maple

with(numtheory): P:= proc(q) local a, b, c, k, m, n; for m from 1 to q do n:=ithprime(m);
a:=n; b:=0; for k from 1 to ilog10(n)+1 do b:=b+(a mod 10^k); od; a:=n; c:=0;
for k from 0 to ilog10(n) do c:=c+trunc(a/10^k); od;
if isprime(b) and isprime(c) then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000040.

Sequence in context: A046705 A054218 A075048 * A230046 A098463 A064155

Adjacent sequences: A281018 A281019 A281020 * A281022 A281023 A281024

Keyword

nonn,easy

Author

Paolo P. Lava, Jan 13 2017

Status

approved