A154500 Sum of any 3 consecutive numbers is prime and |a(n+2) - (a(n+1) + a(n))| is prime, a(1)=3, a(2)=5.
3, 5, 11, 13, 17, 23, 27, 33, 37, 39, 63, 65, 69, 93, 95, 105, 111, 115, 123, 129, 145, 147, 165, 175, 183, 219, 229, 285, 315, 319, 357, 363, 367, 393, 411, 425, 447, 489, 493, 549, 555, 563, 615, 669, 713, 729, 765, 775, 801, 807, 839, 885, 897, 901, 915, 933, 941, 945, 957, 995, 1005, 1023, 1051
Offset: 1
Keywords
Examples
3+5+11=19; 11-(3+5)=3, 5+11+13=29; 13-(5+11)=-3, 11+13+17=41; 17-(11+13)=-7, 13+17+23=53; 23-(13+17)=-7,... .
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Maple
R:= 3,5: count:= 2: a:= 3: b:= 5: for x from b+2 by 2 while count < 100 do if isprime(a+b+x) and isprime(abs(x-(a+b))) then R:= R, x; a:= b; b:= x; count:= count+1; fi od: R; # Robert Israel, Nov 29 2023 -
Mathematica
a=3;b=5;lst={a,b};Do[c=Prime[n];p1=c+a+b;p2=c-(a+b);If[PrimeQ[p1]&&PrimeQ[p2],AppendTo[lst,c];a=b;b=c],{n,5,9!}];lst
Extensions
NAME adapted to offset. - R. J. Mathar, Jun 19 2021
Corrected and extended by Robert Israel, Nov 29 2023
Comments