A337214 Primes prime(k) such that prime(k) + 2*prime(k+1), prime(k) + 2*prime(k+1) + 4*prime(k+2) and prime(k) + 2*prime(k+1) + 4*prime(k+2) + 8*prime(k+3) are all prime.
43, 599, 1451, 8867, 18253, 19211, 19469, 27329, 29863, 40787, 41141, 75403, 85991, 104707, 119921, 131009, 137383, 150551, 167309, 173263, 195977, 201247, 222863, 277961, 285199, 350429, 364333, 374461, 382747, 385783, 406499, 419743, 423803, 466673, 496289, 512821, 532241, 541529, 541579
Offset: 1
Keywords
Examples
a(3)=1451 is in the sequence because 1451, 1453, 1459, 1471 are consecutive primes and 1451+2*1453=4357, 1451+2*1453+4*1459=10193, and 1451+2*1453+4*1459+8*1471=21961 are all prime.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..2000 from Robert Israel)
Programs
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Maple
N:= 60000: # to get terms in the first N primes P:= [seq(ithprime(i), i=1..N+3)]: P[select(i -> isprime(P[i]+2*P[i+1]) and isprime(P[i]+2*P[i+1]+4*P[i+2]) and isprime(P[i]+2*P[i+1]+4*P[i+2]+8*P[i+3]) , [$1..N])];