A244163 Primes which are the concatenation of three consecutive primes p, q, r while the sum (p + q + r) yields another prime.

5711, 111317, 171923, 313741, 414347, 229233239, 389397401, 401409419, 409419421, 449457461, 701709719, 773787797, 787797809, 797809811, 140914231427, 157915831597, 163716571663, 202920392053, 212921312137, 252125312539, 259125932609, 263326472657, 268926932699

Offset: 1

Author

K. D. Bajpai, Jun 21 2014

Keywords

• nonn
• base

Comments

Subsequence of A030469.

The first five terms of this sequence resemble exactly those of A030469.

Examples

			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.
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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2250

Crossrefs

Cf. A000040, A030469, A034961, A034962, A132903.

Programs

Maple

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);

Mathematica

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 *)