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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)). 1

%I

%S 2,3,5,7,137,191,379,421,683,757,919,1001933,1005553,1006091,1012463,

%T 1012513,1013431,1013813,1013921,1013923,1016027,1016401,1016681,

%U 1019657,1022729,1022837,1025537,1028011,1028569,1030069,1030889,1030933,1034069,1038119,1040057

%N 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)).

%H Paolo P. Lava, <a href="/A281021/a281021.txt">First 1000 primes with corresponding x and y</a>

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

%p with(numtheory): P:= proc(q) local a,b,c,k,m,n; for m from 1 to q do n:=ithprime(m);

%p a:=n; b:=0; for k from 1 to ilog10(n)+1 do b:=b+(a mod 10^k); od; a:=n; c:=0;

%p for k from 0 to ilog10(n) do c:=c+trunc(a/10^k); od;

%p if isprime(b) and isprime(c) then print(n); fi; od; end: P(10^9);

%Y Cf. A000040.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Jan 13 2017

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)