A307882 Records of the offset k in A307881, divided by 3.
-1, 1, 3, 5, 7, 9, 11, 13, 15, 25, 29, 31, 39, 45, 61, 63, 75, 81, 85, 111, 123, 131, 151, 175, 207, 225, 241, 267, 301, 329, 335, 427, 435, 505, 539, 565, 611, 617, 665, 695, 739, 805, 843, 875, 1113, 1143, 1465, 1797, 1801, 1959, 2065, 2369, 2783
Offset: 1
Programs
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PARI
kmax=0; for(n=2,10^7,forstep(k=1,n,2,if(isprime(2*n-k)&&isprime(2*n+k),if(k>kmax,if(k%3!=0,print1(-k,", "),print1(k/3,", "));kmax=k);break(1))))
Comments