A278583 Numbers k such that k+1 is a prime, k+2 is twice a prime, and k+3 is three times a prime.

12, 36, 156, 540, 876, 1200, 1380, 1620, 2016, 2556, 2856, 3060, 4356, 4440, 5076, 5580, 5700, 6336, 6636, 6660, 6996, 7416, 8220, 9180, 9660, 9900, 10836, 11496, 12456, 12600, 12720, 12756, 13680, 14436, 15240, 16920, 17076, 18216, 18300, 18396, 19440, 21000, 21576, 22620, 23556, 24480

Offset: 1

Author

N. J. A. Sloane, Nov 30 2016

Keywords

• nonn

Comments

All terms are divisible by 12. - Daniel Poveda Parrilla, Dec 12 2016

References

• R. K. Guy, Posting to Number Theory Mailing List, Nov 30 2016

Links

• Antti Karttunen and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 563 terms from Antti Karttunen)

Crossrefs

Equals A036570(n) - 1.

Positions of terms >= 3 in A278500.

Cf. A074200.

Programs

Mathematica

Select[Range[12,25000,12],AllTrue[{#+1,(#+2)/2,(#+3)/3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 26 2020 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim+1, if(p%6==1 && isprime(p\2+1) && isprime(p\3+1), listput(v,p-1))); Vec(v) \\ Charles R Greathouse IV, Dec 03 2016