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%I #7 Sep 10 2014 12:24:07
%S 157,257,311,353,463,509,691,757,823,839,881,907,941,953,1063,1097,
%T 1223,1229,1249,1297,1301,1307,1439,1459,1531,1583,1669,1723,1777,
%U 1879,1907,1913,1931,2027,2087,2089,2141,2143,2179,2207,2293,2351,2371,2377,2399,2411
%N Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...5, are five primes.
%C Conjecture: only 9198 primes are not in the sequence: 2, 3, ..., 2521081.
%e 157 is in the sequence because with d=30: 127, 97, 67, 37, 7 are all primes.
%t prms = 5; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[2411]]], fQ] (* _T. D. Noe_, Sep 08 2012 *)
%o (PARI) is(n)=my(t); forprime(p=2,n-16,if((n-p)%5==0 && isprime((t=(n-p)/5)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(n), return(1))); 0 \\ _Charles R Greathouse IV_, Sep 10 2014
%Y Cf. A216495, A094383, A216497, A216468.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Sep 08 2012
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