A358572 Smallest prime p in a sexy prime triple such that (p-3)/2 is also the smallest prime in a sexy prime triple (A023241).

17, 97, 1117, 1217, 2897, 130337, 188857, 207997, 221197, 324517, 610817, 900577, 1090877, 1452317, 1719857, 1785097, 2902477, 3069917, 3246317, 4095097, 4536517, 4977097, 5153537, 5517637, 5745557, 6399677, 7168277, 7351957, 7588697, 7661077, 8651537, 8828497, 9153337

Offset

1,1

Comments

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).

Subsequence of A358571.

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

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

Links

Table of n, a(n) for n=1..33.

Example

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.

Mathematica

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

Prog

(PARI)
istriple(p)={isprime(p) && isprime(p+6) && isprime(p+12)}
isok(p)={istriple(p) && istriple((p-3)/2)}
{ forprime(p=1, 10^7, if(isok(p), print1(p, ", "))) } \\ Andrew Howroyd, Dec 30 2022

Crossrefs

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

Sequence in context: A152913 A184327 A331877 * A262207 A282997 A231667

Adjacent sequences: A358569 A358570 A358571 * A358573 A358574 A358575

Keyword

nonn

Author

Lamine Ngom, Nov 23 2022

Status

approved