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%I #20 Aug 08 2021 18:36:49
%S 12720,16920,19440,24480,49680,61560,104160,229320,255360,259680,
%T 266400,291720,298200,311040,331920,419400,423480,436800,446880,
%U 471240,525240,532800,539400,581520,600600,663600,704160,709920,783720,867000,904800,908040,918360
%N Numbers k such that k+1 is a prime, k+2 is twice a prime, k+3 is three times a prime, and k+4 is four times a prime.
%C a(n) == 0 mod 120 (see comment in A163573). - _Chai Wah Wu_, Nov 30 2016
%H Chai Wah Wu, <a href="/A278585/b278585.txt">Table of n, a(n) for n = 1..10001</a>
%t Select[Range[920000],AllTrue[{#+1,(#+2)/2,(#+3)/3,(#+4)/4},PrimeQ]&] (* _Harvey P. Dale_, Aug 08 2021 *)
%o (Python)
%o from sympy import prime, isprime
%o A278585_list = [4*q-4 for q in (prime(i) for i in range(1,10000)) if isprime(4*q-3) and isprime(2*q-1) and (not (4*q-1) % 3) and isprime((4*q-1)//3)] # _Chai Wah Wu_, Nov 30 2016
%o (PARI) is(k)=k%120==0 && isprime(k+1) && isprime(k/2+1) && isprime(k/3+1) && isprime(k/4+1) \\ _Charles R Greathouse IV_, Dec 03 2016
%Y Equals A163573(n) - 1.
%Y Cf. A036570, A074200.
%Y Positions of terms >= 4 in A278500, thus a subsequence of A278583, A089965 and A006093.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Nov 30 2016
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