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 1-6 of 6 results.

A113239 Prime differences of tribonacci numbers.

Original entry on oeis.org

2, 3, 5, 11, 17, 23, 31, 37, 43, 79, 193, 491, 503, 653, 883, 1201, 10607, 19009, 19469, 19489, 34963, 35809, 46499, 223273, 223313, 391231, 409817, 410731, 532159, 634061, 754549, 1383769, 1389533, 2552621, 2555753, 3311233, 4477453, 4700621
Offset: 1

Views

Author

Jonathan Vos Post, Oct 19 2005

Keywords

Comments

A113238 is the difference set of tribonacci numbers. A113188-A113194 deal with difference sets of Fibonacci numbers and Lucas numbers and primes in those difference sets.

Examples

			a(1) = 2 because 4 - 2 = 2 where 4 and 2 are tribonacci numbers.
a(2) = 3 because 7 - 4 = 3 where 7 and 4 are tribonacci numbers.
a(3) = 5 because 7 - 2 = 5 where 7 and 2 are tribonacci numbers.
a(4) = 11 because 13 - 2 = 11 where 13 and 2 are tribonacci numbers.
a(5) = 17 because 24 - 7 = 17 where 24 and 7 are tribonacci numbers.

Crossrefs

Cf. A000040, A000073, A113188-A113194, A113238.

Programs

  • Mathematica
    Select[Union[Flatten[Differences/@Subsets[Drop[LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 29],2],{2}]]],PrimeQ] (* James C. McMahon, Jun 23 2024 *)

Formula

Intersection of primes A000040 and difference set of tribonacci numbers A113238. Positive prime values of {A000073(i) - A000073(j) such that i>j}.

A113244 Prime differences of tetranacci numbers.

Original entry on oeis.org

2, 3, 7, 11, 13, 41, 79, 107, 179, 193, 293, 397, 769, 1489, 2099, 2843, 2857, 5507, 5521, 9181, 10463, 10663, 10667, 19079, 39619, 76423, 126743, 146539, 147283, 147311, 281081, 283949, 547229, 771073, 3919171, 3919543, 3919943, 7555879, 7555927, 10644589, 14564477
Offset: 1

Views

Author

Jonathan Vos Post, Oct 19 2005; corrected Oct 20 2005

Keywords

Comments

A113188-A113194 deal with difference sets of Fibonacci numbers and Lucas numbers and primes in those difference sets. A113238-A113239 deal with the difference set of tribonacci numbers and primes in that difference set.

Examples

			a(1) = 2 because 4 - 2 = 2 where 4 and 2 are tetranacci numbers.
a(2) = 3 because 4 - 1 = 3 where 4 and 1 are tetranacci numbers.
a(3) = 7 because 8 - 1 = 7 where 8 and 1 are tetranacci numbers.
a(4) = 11 because 15 - 4 = 11 where 15 and 4 are tetranacci numbers.
a(5) = 13 because 15 - 2 = 13 where 15 and 2 are tetranacci numbers.

Crossrefs

Cf. A000040, A000078, A113188-A113194, A113238, A113239, A113243.

Programs

  • Maple
    isA113244 := proc(n)
    isprime(n) and isA113243(n) ;
end proc:
for n from 1 do
    p := ithprime(n) ;
    if isA113244(p) then
        printf("%d\n",p) ;
    end if;
end do: # R. J. Mathar, Oct 04 2014

Formula

{a(n)} = intersection of A000040 and A113243. {a(n)} = primes in the difference set of tetranacci sequence A000078, excluding prime tetranacci numbers A104535.

Extensions

281081 inserted by R. J. Mathar, Oct 04 2014

A113193 Number of times that Lucas(n)-Lucas(i) is prime for i=0..n-3.

Original entry on oeis.org

1, 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 1, 1, 2, 0, 1, 0, 1, 3, 1, 0, 2, 2, 1, 3, 1, 0, 1, 0, 3, 3, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 0, 4, 2, 1, 3, 0, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 1, 3, 0, 2, 1, 2, 1, 0, 0, 2, 3, 0, 1, 1, 3, 0, 1, 0, 1, 0, 0, 4, 1, 1, 1, 2, 1, 0, 1, 0, 3, 1, 1, 0, 2, 4, 1, 1, 0, 3, 0, 0, 5, 0, 1, 2, 1, 0
Offset: 3

Views

Author

T. D. Noe, Oct 17 2005

Keywords

Comments

We exclude i=n-2 and i=n-1 because they yield Lucas(n-2) and Lucas(n-1), respectively. Sequence A113194 lists the n for which a(n)=0.

Crossrefs

Cf. A113192 (primes that are the difference of two Lucas numbers).

Programs

  • Mathematica
    Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; Table[cnt=0; Do[If[PrimeQ[Lucas[n]-Lucas[i]], cnt++ ], {i, 0, n-3}]; cnt, {n, 3, 150}]

A113293 First differences of Lucas 3-step numbers.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 14, 18, 20, 28, 32, 36, 38, 50, 60, 64, 68, 70, 92, 110, 120, 124, 128, 130, 170, 202, 220, 230, 234, 238, 240, 312, 372, 404, 422, 432, 436, 440, 442, 574, 684, 744, 776, 794, 804, 808, 812, 814, 1056, 1258, 1368, 1428, 1460, 1478, 1488
Offset: 1

Views

Author

Jonathan Vos Post, Oct 23 2005

Keywords

Comments

There are no primes in this sequence, except 2, as all values are odd, so all differences are even. Semiprimes include: a(3) = 4, a(4) = 6, a(6) = 10, a(7) = 14, a(13) = 38, a(26) = 202, a(35) = 422, a(44) = 794, a(54) = 1478, a(59) = 1942, a(66) = 2746, a(94) = 9326.

Examples

			a(0) = 0 because A001644(2)-A001644(0) = 3 - 3 = 0.
a(1) = 2 because A001644(2)-A001644(1) = 3 - 1 = 2.
a(2) = 4 because A001644(3)-A001644(2) = 7 - 3 = 4.
a(3) = 6 because A001644(3)-A001644(1) = 7 - 1 = 6.
a(75) = 5000 because A001644(14)-A001644(7) = 5071 - 71 = 5000.

Links

Crossrefs

Cf. A000040, A001358, A001644, A113188-A113194, A113238, A113239, A113244.

Formula

{a(n)} = { | A001644(i) - A001644(j) | such that i>=j}

A113294 First differences of Lucas 4-step numbers.

Original entry on oeis.org

1, 3, 4, 8, 11, 12, 19, 22, 23, 25, 36, 44, 47, 48, 73, 84, 92, 95, 96, 140, 165, 176, 184, 187, 188, 268, 316, 341, 352, 360, 363, 364, 517, 609, 657, 682, 693, 701, 704, 705, 998, 1174, 1266, 1314, 1339, 1350, 1358, 1361, 1362, 1923, 2264, 2440, 2532, 2580
Offset: 1

Views

Author

Jonathan Vos Post, Oct 23 2005

Keywords

Comments

Lucas 4-step numbers are also known as "Tetranacci Lucas numbers" or "Tetranacci numbers with different initial conditions" in A073817. Primes in this sequence are A113295. In this sequence are: 13340261 = 11 * 19 * 29 * 31 * 71 is a product of 5 distinct 2-digit primes; 95550683 = 269 * 593 * 599 is a product of 3 distinct 3-digit primes.

Examples

			a(0) = 1 because A073817(0)-A001644(2) = 4 - 3 = 1.
a(1) = 3 because A073817(3)-A001644(0) = 7 - 4 = 3.
a(2) = 4 because A073817(3)-A001644(2) = 7 - 3 = 4.
a(3) = 8 because A073817(4)-A001644(3) = 15 - 7 = 8.
a(122) = 70000 because A073817(17)-A001644(3) = 70007 - 7 = 70000.

Links

Crossrefs

Cf. A000040, A073817, A113188-A113194, A113238, A113239, A113244, A113293, A113295.

Formula

{a(n)} = { | A073817(i) - A073817(j) | such that i>=j }

A113295 Prime differences of Lucas 4-step numbers.

Original entry on oeis.org

3, 11, 19, 23, 47, 73, 701, 1361, 4363, 9067, 9749, 17477, 18743, 18839, 36293, 70003, 116101, 134917, 366437, 465061, 498749, 501013, 1844033, 3590099, 13305307, 13341259, 13341619, 36229121, 49069367, 49570721, 95550661, 351427309
Offset: 1

Views

Author

Jonathan Vos Post, Oct 23 2005

Keywords

Comments

These are primes from the sequence A113294, which is differences of Lucas 4-step numbers, also known as "Tetranacci Lucas numbers" or "Tetranacci numbers with different initial conditions" in A073817. Also in the difference set sequence are: 13340261 = 11 * 19 * 29 * 31 * 71 is a product of 5 distinct 2-digit primes; 95550683 = 269 * 593 * 599 is a product of 3 distinct 3-digit primes.

Examples

			a(1) = 3 because A073817(0)-A001644(1) = 4 - 1 = 3, a prime.
a(2) = 11 because A073817(4)-A001644(0) = 15 - 4 = 11, a prime.
a(3) = 19 because A073817(5)-A001644(3) = 26 - 7 = 19, a prime.
a(4) = 23 because A073817(5)-A001644(2) = 26 - 3 = 23, a prime.
a(16) = 70003 because A073817(17)-A001644(0) = 70007 - 4 = 70003, a prime.

Links

Crossrefs

Cf. A000040, A073817, A113188-A113194, A113238, A113239, A113244, A113293, A113294.

Formula

{a(n)} = Intersection of { | A073817(i) - A073817(j) | such that i>=j} and A000040. {a(n)} = Prime elements of { | A073817(i) - A073817(j) | such that i>=j}. {a(n)} = Prime elements of A113294.
Showing 1-6 of 6 results.

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