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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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,... .

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

Crossrefs

Cf. A154484, A154485, A154486, A154487, A154488, A154493, A154494, A154495, A154496, A062391, A154497, A154498.

Sequence in context: A076757 A178942 A045404 * A152460 A130097 A020612

Adjacent sequences: A154497 A154498 A154499 * A154501 A154502 A154503

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 10 2009

Extensions

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

Corrected and extended by Robert Israel, Nov 29 2023

Status

approved