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
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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 *)
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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
A153866
Largest of four consecutive Fibonacci numbers whose sum is a prime number.
Original entry on oeis.org
3, 5, 13, 21, 89, 233, 987, 1597, 4181, 1346269, 24157817, 165580141, 2971215073, 53316291173, 2504730781961, 308061521170129, 14472334024676221, 184551825793033096366333
Offset: 1
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a=0;b=1;c=1;lst={};Do[d=Fibonacci[n];p=a+b+c+d;If[PrimeQ[p],AppendTo[lst,d]];a=b;b=c;c=d,{n,3,6!}];lst
Alternate: Transpose[Select[Partition[Fibonacci[Range[200]],4,1],PrimeQ[Plus@@#]&]][[4]] (* Harvey P. Dale, Dec 05 2010 *)
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
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
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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 *)
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
-
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
Cf.
A000045,
A001906,
A000071,
A001605,
A153862,
A153863,
A153865,
A153866,
A153867,
A153887,
A153888.
-
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
Cf.
A000045,
A001906,
A000071,
A001605,
A153862,
A153863,
A153865,
A153866,
A153867,
A153887,
A153888,
A153889
-
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
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.
- Harvey P. Dale, Table of n, a(n) for n = 1..29
- Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, Primes and composites in the determinant Hosoya triangle, arXiv:2211.10788 [math.NT], 2022.
- Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, Primes and composites in the determinant Hosoya triangle, The Fibonacci Quarterly, 60.5 (2022), 56-110.
Cf.
A000045,
A001906,
A000071,
A001605,
A013655,
A153862,
A153863,
A153865,
A153866,
A153867,
A153887,
A153888,
A153889,
A153890,
A153891.
-
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
Cf.
A000045,
A001906,
A000071,
A001605,
A153862,
A153863,
A153865,
A153866,
A153867,
A153887,
A153888,
A153889,
A153890.
-
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 *)
Showing 1-8 of 8 results.
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