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A179769 Number of steps for the map of primes p -> 4p + 3, starting at the n-th prime == 3 (mod 4), needed to reach the final prime in the trajectory. 0
0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 3, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 3, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The maximum number of iterations is 8 (proof in A179767).

The similar problem with the map p -> 4p + 1 is less interesting because that sequence contains numbers <= 1: if we consider just the first two iterations 4p + 1 -> 16p + 5 -> 64p + 21, then (i) if p==0 (mod 3), 64p + 21 is composite, (ii) if p==1 (mod 3), 16p + 5 is composite and (iii) if p==2 (mod 3), 4p + 1 is composite. Thus the maximum number of iterations is 1.

LINKS

Table of n, a(n) for n=0..113.

EXAMPLE

a(1) = 0 because the first prime == 3 (mod 4) is A002145(1) = 3 and 3*4 + 3 = 15 is composite.

a(2) = 2 because the second prime == 3 (mod 4) is A002145(2) = 7, and 4*7 + 3 = 31 -> 4*31 + 3 = 127 are primes.

a(1761) = 8 because the 1761st prime == 3 (mod 4) is A002145(1761) = 32611 and 32611 -> 130447 -> 521791 -> 2087167 -> 8348671 -> 33394687 -> 133578751 -> 534315007 -> 2137260031 are primes.

MAPLE

with(numtheory):for i from 1 to 300 do : n:=ithprime(i):if irem(n, 4) = 3 then

nn:=n: id:=0:k:=0:for it from 1 to 8 do: p:=4*nn+3: if type (p, prime)=true and

id=0 then k:=k+1:nn:=p:else id:=1:fi:od:printf(`%d, `, k):else fi:od:

CROSSREFS

Cf. A002144, A002145, A179767.

Sequence in context: A074080 A347687 A287331 * A340594 A227193 A287397

Adjacent sequences: A179766 A179767 A179768 * A179770 A179771 A179772

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 10 2011

STATUS

approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)