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A103388 Primes in A103378. 3
2, 3, 5, 7, 17, 31, 71, 127, 157, 227, 257, 293, 349, 419, 503, 32299, 33343, 72421, 80429, 134269, 140473, 252761, 2499061, 201329923, 607488611, 1005428989, 2920552289, 8185638173, 10676478541, 14058719281, 15985335181, 34020175663, 159315910211, 1448256661853 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are the unique primes that are found in the k=10 case of the family of sequences whose k=1 case is the Fibonacci sequence A000045, k=2 case is the Padovan sequence A000931 (offset so as to begin 1,1,1), k=3 case is A079398 (offset so as to begin 1,1,1,1), k=4 case is A103372, k=5 case is A103373, k=6 case is A103374, k=7 case is A103375, k=8 case is A103376, k=9 case is A103377 and k=11 case is A103379. The general case for integer k>1 is defined: a(1) = a(2) = ... = a(k+1) = 1 and for n>k+1, a(n) = a(n-k) + a(n-[k+1]). For this k=10 case, the ratio of successive terms a(n)/a(n-1) approaches the unique positive root of the characteristic polynomial: x^11 - x - 1 = 0. This is the real constant 1.068297188920841276369429588323878282093631016920833444507611946647... . Note that x = (1 + (1 + (1 + (1 + (1 + ...)^(1/11))^(1/11)))^(1/11))))^(1/11)))))^(1/11))))). This sequence of prime values in this k=10 case is A103388. The sequence of semiprime values in this k=10 case is A103398.

N.B.: a(n) in the above does not refer to the terms of this sequence. - M. F. Hasler, Sep 19 2015

LINKS

Table of n, a(n) for n=1..34.

FORMULA

Intersection of A103378 with A000040. A103378 is defined: a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = a(10) = a(11) = 1 and for n>11: a(n) = a(n-10) + a(n-11).

MAPLE

A103378 := proc(n) option remember ; if n <= 11 then 1; else procname(n-10)+procname(n-11) ; fi; end: isA103378 := proc(n) option remember ; local i ; for i from 1 do if A103378(i) = n then RETURN(true) ; elif A103378(i) > n then RETURN(false) ; fi; od: end: A103388 := proc(n) option remember ; local a; if n = 1 then 2; else a := nextprime(procname(n-1)) ; while true do if isA103378(a) then RETURN(a) ; fi; a := nextprime(a) ; od: fi; end: for n from 1 to 37 do printf("%d, ", A103388(n)) ; od: # R. J. Mathar, Aug 30 2008

MATHEMATICA

Clear[a]; k=10; Do[a[n]=1, {n, k+1}]; a[n_]:=a[n]=a[n-k]+a[n-k-1]; A103387=Union[Select[Array[a, 1000], PrimeQ]] (* See A103377 and A103397 for code related to those. - M. F. Hasler, Sep 19 2015, . *)

PROG

(PARI) {a=vector(m=10, n, 1); L=0; for(n=m, 10^5, isprime(a[i=n%m+1]+=a[(n+1)%m+1]) && L<a[i] && print1(L=a[i]", "))} \\ M. F. Hasler, Sep 19 2015

CROSSREFS

Cf. A000045, A000931, A079398, A103372-A103381, A103378, A103398.

Sequence in context: A103385 A103389 A103387 * A103386 A103384 A103383

Adjacent sequences:  A103385 A103386 A103387 * A103389 A103390 A103391

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 15 2005

EXTENSIONS

Corrected from a(16) on by R. J. Mathar, Aug 30 2008

Edited and more terms added by M. F. Hasler, Sep 19 2015

STATUS

approved

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Last modified May 8 11:51 EDT 2021. Contains 343666 sequences. (Running on oeis4.)