cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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

Original entry on oeis.org

7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771, 258899611203303418721656157249445530046830073044201152332257717521
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

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

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

A153887 Smallest of five consecutive Fibonacci numbers whose sum is a prime number.

Original entry on oeis.org

0, 1, 2, 8, 89, 144, 2584, 121393, 196418, 832040, 20365011074, 4052739537881, 8944394323791464, 99194853094755497, 2880067194370816120, 14028366653498915298923761, 96151855463018422468774568
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Examples

			For n=3,4, the Fibonacci indices of a(3)=2, a(4)=8, are 3,6 respectively. So a(3) + A000032(7)= 31,  a(4) + A000032(10) = 131. - _Vladimir Shevelev_, Apr 24 2014

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867.

Programs

  • Mathematica
    a=0;b=1;c=1;d=2;lst={};Do[e=Fibonacci[n];p=a+b+c+d+e;If[PrimeQ[p],AppendTo[lst,a]];a=b;b=c;c=d;d=e,{n,4,6!}];lst
Select[Partition[Fibonacci[Range[1000]],5,1],PrimeQ[Total[#]]&][[All,1]] (* Harvey P. Dale, Dec 01 2016 *)

Formula

For n>=3, a(n) + A000032(m+4) is prime, where m is the Fibonacci index of a(n) (see example). This follows from the identity F(m+1) + F(m+2) + F(m+3) + F(m+4) = A000032(m+4), m>=0. - Vladimir Shevelev, Apr 24 2014

A153888 Second-to-smallest of five consecutive Fibonacci numbers such that sum of five consecutive Fibonacci numbers is prime number.

Original entry on oeis.org

1, 2, 3, 13, 144, 233, 4181, 196418, 317811, 1346269, 32951280099, 6557470319842, 14472334024676221, 160500643816367088, 4660046610375530309, 22698374052006863956975682, 155576970220531065681649693
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Links

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867, A153887

Programs

  • Mathematica
    a=0;b=1;c=1;d=2;lst={};Do[e=Fibonacci[n];p=a+b+c+d+e;If[PrimeQ[p],AppendTo[lst,b]];a=b;b=c;c=d;d=e,{n,4,6!}];lst
Select[Partition[Fibonacci[Range[0,150]],5,1],PrimeQ[Total[#]]&][[All,2]] (* Harvey P. Dale, Dec 11 2018 *)

A153889 Middle of five consecutive Fibonacci numbers such that sum of five consecutive Fibonacci numbers is prime number.

Original entry on oeis.org

1, 3, 5, 21, 233, 377, 6765, 317811, 514229, 2178309, 53316291173, 10610209857723, 23416728348467685, 259695496911122585, 7540113804746346429, 36726740705505779255899443, 251728825683549488150424261, 37281903592600898879479448409585328515842582885579275203077366912825
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867, A153887, A153888.

Programs

  • Mathematica
    a=0;b=1;c=1;d=2;lst={};Do[e=Fibonacci[n];p=a+b+c+d+e;If[PrimeQ[p],AppendTo[lst,c]];a=b;b=c;c=d;d=e,{n,4,6!}];lst

A153890 Second-to-largest of five consecutive Fibonacci numbers such that sum of five consecutive Fibonacci numbers is prime number.

Original entry on oeis.org

2, 5, 8, 34, 377, 610, 10946, 514229, 832040, 3524578, 86267571272, 17167680177565, 37889062373143906, 420196140727489673, 12200160415121876738, 59425114757512643212875125
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867, A153887, A153888, A153889

Programs

  • Mathematica
    a=0;b=1;c=1;d=2;lst={};Do[e=Fibonacci[n];p=a+b+c+d+e;If[PrimeQ[p],AppendTo[lst,d]];a=b;b=c;c=d;d=e,{n,4,6!}];lst

A153892 Primes that are the sum of five consecutive Fibonacci numbers.

Original entry on oeis.org

7, 19, 31, 131, 1453, 2351, 42187, 1981891, 3206767, 13584083, 332484016063, 66165989928299, 146028309791690867, 1619478772188347101, 47020662244482792763, 229030451631542624193448579, 1569798068858809572115420691
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

Primes of the form F(k+3)+L(k+2), where F(k) and L(k) are the k-th Fibonacci number and Lucas number, respectively. This formula also gives that 3,2 and 5 are primes of the form F(k+3)+L(k+2), with k=-2, k=-1, k=0, respectively. - Rigoberto Florez, Jul 31 2022
Are there infinitely many primes of the form F(k+3)+L(k+2)? There are 47 primes of this form for k <= 80000. There are no such primes for 64000 <= k <= 80000. - Rigoberto Florez, Feb 26 2023
a(29) has 948 digits; a(30) has 1253 digits. - Harvey P. Dale, Jan 13 2013

Examples

			a(1) =  7 = 0+1+1+2+3 is prime;
a(2) = 19 = 1+2+3+5+8 is prime;
a(3) = 31 = 2+3+5+8+13 is prime, etc.

Links

Crossrefs

Cf. A000045, A001906, A000071, A001605, A013655, A153862, A153863, A153865, A153866, A153867, A153887, A153888, A153889, A153890, A153891.

Programs

  • Mathematica
    Select[Total/@Partition[Fibonacci[Range[0,150]],5,1],PrimeQ] (* Harvey P. Dale, Jan 13 2013 *)

A153891 Largest of five consecutive Fibonacci numbers such that the sum of the five consecutive Fibonacci numbers is prime.

Original entry on oeis.org

3, 8, 13, 55, 610, 987, 17711, 832040, 1346269, 5702887, 139583862445, 27777890035288, 61305790721611591, 679891637638612258, 19740274219868223167, 96151855463018422468774568, 659034621587630041982498215, 97605290770725966021179803308812675106786783237939047196728424115618
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Keywords

Comments

0+1+1+2=3=7, 1+2+3+5+8=19, 2+3+5+8=13=31, 8+13+21+34+55=131, 89+144+233+377+610=1453, 144+233+377+610+987=2351,...

Crossrefs

Cf. A000045, A001906, A000071, A001605, A153862, A153863, A153865, A153866, A153867, A153887, A153888, A153889, A153890.

Programs

  • Mathematica
    a=0;b=1;c=1;d=2;lst={};Do[e=Fibonacci[n];p=a+b+c+d+e;If[PrimeQ[p],AppendTo[lst,e]];a=b;b=c;c=d;d=e,{n,4,6!}];lst
Transpose[Select[Partition[Fibonacci[Range[0,400]],5,1],PrimeQ[ Total[ #]]&]][[5]] (* Harvey P. Dale, Nov 14 2011 *)

Extensions

One more term (a(17)) from Harvey P. Dale, Nov 14 2011
a(18) from Alois P. Heinz, Aug 31 2025
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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