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A113295 Prime differences of Lucas 4-step numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..32.

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.

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.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A030377 A092060 A071916 * A043433 A078583 A017101

Adjacent sequences:  A113292 A113293 A113294 * A113296 A113297 A113298

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 23 2005

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)