A153890 -id:A153890 - cp's OEIS frontend

A181491 Primes of the form p = 3*2^k - 1 such that p+2 is also prime.

5, 11, 191, 786431

Offset: 1

M. F. Hasler, Oct 30 2010

Sequence A181490 lists the exponents k, sequences A181492 and A181493 the corresponding upper twin prime and their average.

a(5) > 3 * 2 ^ 3000 + 1. - Max Z. Scialabba, Dec 24 2023

Cf. A001097, A001359, A006512, A014574.

PARI
```
for( k=1,999, ispseudoprime(3<
				
```

A181491 = A007283 intersect A014574 = A181492 - 2 = A181493 - 1 = 3*2^A153890 - 1.

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

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

nonn

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

			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

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

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,...

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 *)

One more term (a(17)) from Harvey P. Dale, Nov 14 2011

a(18) from Alois P. Heinz, Aug 31 2025

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A181491 Primes of the form p = 3*2^k - 1 such that p+2 is also prime.

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

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

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