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%I #15 Jan 05 2021 14:58:45
%S 5711,111317,171923,313741,414347,229233239,389397401,401409419,
%T 409419421,449457461,701709719,773787797,787797809,797809811,
%U 140914231427,157915831597,163716571663,202920392053,212921312137,252125312539,259125932609,263326472657,268926932699
%N Primes which are the concatenation of three consecutive primes p, q, r while the sum (p + q + r) yields another prime.
%C Subsequence of A030469.
%C The first five terms of this sequence resemble exactly those of A030469.
%H K. D. Bajpai, <a href="/A244163/b244163.txt">Table of n, a(n) for n = 1..2250</a>
%e 5711 is in the sequence because the concatenation of [5, 7, 11] = 5711 which is prime. The sum [5 + 7 + 11] = 23 is another prime.
%e 111317 is in the sequence because the concatenation of [11, 13, 17] = 111317 which is prime. The sum [11 + 13 + 17] = 41 is another prime.
%p A244163:= proc() local a,b,c,k,m; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); m:=a+b+c; k:=parse(cat(a,b,c)); if isprime(k) and isprime(m) then RETURN (k); fi; end: seq(A244163 (), n=1..500);
%t prQ[{a_,b_,c_}]:=Module[{p=FromDigits[Flatten[IntegerDigits/@ {a,b,c}]]}, If[ AllTrue[ {p,a+b+c},PrimeQ],p,Nothing]]; prQ/@Partition[ Prime[ Range[ 500]],3,1] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 05 2021 *)
%Y Cf. A000040, A030469, A034961, A034962, A132903.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Jun 21 2014
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