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A342180 a(1)=2, a(2)=3, a(n+1) is the smallest prime obtainable using the Fibonacci recurrence, with a(n-1) and a(n-2) as start terms. 0
2, 3, 5, 13, 31, 313, 2659, 96979, 97340263, 96133996771, 288596670839, 35613385860024917251, 1210855125301377274153, 41916955363307350583473, 15591408363472449707385195674347327, 1169745412471464144682860140699762684239, 3996415043088150608161205763193030023888222461378463323 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

33 terms have been calculated; the last, having 13189 decimal digits, required 25197 iterations to compute. It is not known if the sequence continues beyond a(33).

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

a(1)+a(2)=2+3=5, so a(3)=5.

a(2)+a(3)=3+5=8 and 5+8=13, so a(4)=13.

MATHEMATICA

Block[{a = {2, 3}, j, k, s}, Do[Set[{j, k}, a[[-2 ;; -1]]]; While[! PrimeQ[Set[s, j + k]], Set[{j, k}, {k, s}]]; AppendTo[a, s], {i, Length@ a + 1, 12}]; a] (* Michael De Vlieger, Mar 04 2021 *)

PROG

(Python)

from sympy import isprime

def aupton(terms):

  alst = [2, 3]

  for n in range(3, terms+1):

    fnm2, fnm1 = alst[-2:]

    while not isprime(fnm2 + fnm1): fnm2, fnm1 = fnm1, fnm2+fnm1

    alst.append(fnm2 + fnm1)

  return alst

print(aupton(16)) # Michael S. Branicky, Mar 04 2021

CROSSREFS

Cf. A000045, A005478.

Sequence in context: A060434 A175093 A072999 * A345076 A233515 A173268

Adjacent sequences:  A342177 A342178 A342179 * A342181 A342182 A342183

KEYWORD

nonn

AUTHOR

David James Sycamore, Mar 04 2021

STATUS

approved

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Last modified January 24 18:30 EST 2022. Contains 350565 sequences. (Running on oeis4.)