

A113295


Prime differences of Lucas 4step 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
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OFFSET

1,1


COMMENTS

These are primes from the sequence A113294, which is differences of Lucas 4step 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 2digit primes; 95550683 = 269 * 593 * 599 is a product of 3 distinct 3digit primes.


LINKS

Table of n, a(n) for n=1..32.
Eric Weisstein's World of Mathematics, Lucas nStep Number.
Noe, T. D. and Post, J. V., Primes in Fibonacci nstep and Lucas nStep 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, A113188A113194, 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



