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A244163 Primes which are the concatenation of three consecutive primes p, q, r while the sum (p + q + r) yields another prime. 2
5711, 111317, 171923, 313741, 414347, 229233239, 389397401, 401409419, 409419421, 449457461, 701709719, 773787797, 787797809, 797809811, 140914231427, 157915831597, 163716571663, 202920392053, 212921312137, 252125312539, 259125932609, 263326472657, 268926932699 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 17:01 EDT 2021. Contains 343050 sequences. (Running on oeis4.)