A113293 -id:A113293 - cp's OEIS frontend

A113294 First differences of Lucas 4-step numbers.

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

Jonathan Vos Post, Oct 23 2005

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.

			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.

Eric Weisstein's World of Mathematics, Lucas n-Step Number.
Noe, T. D. and Post, J. V., Primes in Fibonacci n-step and Lucas n-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005.

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

{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

Jonathan Vos Post, Oct 23 2005

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.

			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.

Eric Weisstein's World of Mathematics, Lucas n-Step Number.
Noe, T. D. and Post, J. V., Primes in Fibonacci n-step and Lucas n-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005.

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

{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.

cp's OEIS Frontend

A113294 First differences of Lucas 4-step numbers.

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