A153128 Prime numbers such that the sum of any 2 or 4 consecutive terms are averages of twin prime pairs and sum of any 3 or 5 consecutive terms are primes.
11, 31, 41, 67, 131, 3121, 4229, 13159, 14081, 24631, 49877, 64921, 71789, 127051, 154871, 178621, 249677, 260011, 350729, 401473, 487397, 537883, 567767, 718423, 724499, 763621, 1004987, 1016611, 1043951, 1053529, 1090949, 1295113, 1309907
Offset: 1
Keywords
Programs
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Mathematica
a=11;b=31;c=41;d=67;lst={a,b,c,d};Do[z=a+b+c+d+n;y=c+d+n;If[PrimeQ[z]&&n>d&&PrimeQ[n]&&PrimeQ[y]&&PrimeQ[a+b-1]&&PrimeQ[a+b+1]&&PrimeQ[b+c-1]&&PrimeQ[b+c+1]&&PrimeQ[c+d-1]&&PrimeQ[c+d+1]&&PrimeQ[d+n-1]&&PrimeQ[d+n+1]&&PrimeQ[a+b+c+d-1]&&PrimeQ[a+b+c+d+1]&&PrimeQ[b+c+d+n-1]&&PrimeQ[b+c+d+n+1],AppendTo[lst,n];a=b;b=c;c=d;d=n],{n,0,10!}];lst