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

1,1

Comments

Subsequence of A030469.

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A237743 A025027 A030469 * A253423 A202376 A330208

Adjacent sequences: A244160 A244161 A244162 * A244164 A244165 A244166

Keyword

nonn,base

Author

K. D. Bajpai, Jun 21 2014

Status

approved