A174858 - OEIS

%I #9 Aug 17 2024 22:28:01

%S 5,11,17,41,11171,16061,16187,20897,29021,34841,36011,39227,41177,

%T 51341,55331,56891,58907,63311,64151,69191,77261,82757,113021,122027,

%U 123731,135461,151337,167621,173291,174761,187631,191447,195731,203207,203381,225341,227531

%N Primes p of a prime triple (p,p+2,p+6) such that the concatenation p//(p+2)//(p+6) is prime.

%C If p is a d-digit prime of a triple: p*10^(2*d) + (p+2)*10^d + p+6 = (10^(2*d)+10^d+1) * p + 2*(10^d+3) to be a prime.

%C No such concatenation exists for a 4-digit p: d=4, p*10^8 + (p+2)*10^4 + p+6 = p*(10^8 + 10^4 + 1) + 2*10^4 + 6, coefficients (10^8 + 10^4 + 1) and 2*(10^4 + 3) have both divisor 7.

%H Harvey P. Dale, <a href="/A174858/b174858.txt">Table of n, a(n) for n = 1..1000</a>

%e (5,7,11) is 1st prime triple, 5711 = prime(752), 5 is 1st term of sequence

%e (11,13,17) is 2nd prime triple, 111317 = prime(10561), 11 is 2nd term of sequence

%t Transpose[Select[Partition[Prime[Range[20000]],3,1],Differences[#]=={2,4} && PrimeQ[ FromDigits[Flatten[IntegerDigits/@#]]]&]][[1]] (* _Harvey P. Dale_, Apr 10 2013 *)

%Y Cf. A022004.

%K base,nonn,uned

%O 1,1

%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 31 2010