A154493 a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(1)=1,a(2)=4.

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, ...

Links

Table of n, a(n) for n=1..42.

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

Cf. A154484, A154485, A154486, A154487, A154488

Sequence in context: A267103 A030553 A304567 * A337519 A031012 A349428

Adjacent sequences: A154490 A154491 A154492 * A154494 A154495 A154496

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Extensions

NAME adapted to offset. - R. J. Mathar, Jun 19 2021

Status

approved