A153867 Primes which are the sum of four consecutive Fibonacci numbers.

7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

• nonn

Comments

1+1+2+3=7, 1+2+3+5=11, 3+5+8+13=29, 5+8+13+21=47, 21+34+55+89=199,...

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..28
• Harvey P. Dale and others, A005479 and A153867, SeqFan list, Apr 24 2014.

Crossrefs

Cf. A001906, A000071, A001605, A153862, A153863, A153865, A153866.

Primes >3 of A000032 and of A000204.

Programs

Mathematica

a=0;b=1;c=1;lst={};Do[d=Fibonacci[n];p=a+b+c+d;If[PrimeQ[p],AppendTo[lst,p]];a=b;b=c;c=d,{n,3,6!}];lst
Select[Total/@Partition[Fibonacci[Range[500]],4,1],PrimeQ] (* Harvey P. Dale, Apr 23 2014 *)

PARI

list(lim)=my(v=List(),a=7,b=11); while(a<=lim, if(isprime(a), listput(v,a)); [a,b]=[b,a+b]); Vec(v) \\ Charles R Greathouse IV, Oct 07 2016

Formula

a(n) = A005479(n+2). - R. J. Mathar, Jan 05 2009 [See also link to the SeqFan list. - M. F. Hasler, Apr 24 2014]

Extensions

One additional term (a(19)) from Harvey P. Dale, Apr 23 2014