A358572 - OEIS

%I #18 Dec 31 2022 15:28:43

%S 17,97,1117,1217,2897,130337,188857,207997,221197,324517,610817,

%T 900577,1090877,1452317,1719857,1785097,2902477,3069917,3246317,

%U 4095097,4536517,4977097,5153537,5517637,5745557,6399677,7168277,7351957,7588697,7661077,8651537,8828497,9153337

%N Smallest prime p in a sexy prime triple such that (p-3)/2 is also the smallest prime in a sexy prime triple (A023241).

%C Also numbers m such that m-4, m-1, m+5, m+8, m+11 and m+20 cannot be represented as x*y + x + y, with x >= y > 1 (A254636).

%C Subsequence of A358571.

%C Number of terms < 10^k: 0, 2, 2, 5, 5, 12, 34, 150, 655, ...

%C All terms p and (p-3)/2 have a final decimal digit of 7. This follows from considering possibilities modulo 10 and implies p + 18 and (p-3)/2 + 18 are divisible by 5 and hence composite. Both p and (p-3)/2 are therefore also terms of A046118. - _Andrew Howroyd_, Dec 31 2022

%e 97 is the smallest prime in the sexy prime triple (97, 103, 109), and the triple (47 = (97 - 3)/2, 47 + 6, 47 + 12) forms another sexy prime triple. Hence 97 is in the sequence.

%t Select[Prime[Range[700000]], AllTrue[Join[# + {6,12}, (#-3)/2 + {0, 6, 12}], PrimeQ] &] (* _Amiram Eldar_, Nov 23 2022 *)

%o (PARI)

%o istriple(p)={isprime(p) && isprime(p+6) && isprime(p+12)}

%o isok(p)={istriple(p) && istriple((p-3)/2)}

%o { forprime(p=1,10^7,if(isok(p), print1(p, ", "))) } \\ _Andrew Howroyd_, Dec 30 2022

%Y Cf. A023201, A023241, A046118, A255361, A254636, A256386, A358571.

%K nonn

%O 1,1

%A _Lamine Ngom_, Nov 23 2022