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A154493
a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=1,a(2)=4.
8
1, 4, 15, 28, 39, 50, 81, 350, 459, 512, 675, 944, 987, 1040, 1917, 1936, 2325, 2378, 2421, 2588, 2745, 2812, 3459, 3488, 3495, 3506, 5667, 5804, 6027, 6074, 24765, 24832, 25479, 25552, 27621, 27848, 27951, 27980, 34101, 34720, 34773, 35344
OFFSET
1,2
COMMENTS
Sum and difference of any of two consecutive numbers in current sequence are prime numbers and multiplication and any two consecutive numbers is Average of twin prime pairs : 4-1=3;4+1=5;4*1=4, 15-4=11;15+4=19;15*4=60, ...
MATHEMATICA
a=1; b=4; lst={a, b}; Do[If[PrimeQ[n-b]&&PrimeQ[n+b]&&PrimeQ[n*b-1]&&PrimeQ[n*b+1], AppendTo[lst, n]; a=b; b=n], {n, b+1, 9!}]; lst
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
NAME adapted to offset. - R. J. Mathar, Jun 19 2021
STATUS
approved