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A223175 Smallest prime q such that 2n+1 = p + 8*q for some odd prime p, or 0 if no such prime exists. 4
0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 3, 2, 2, 3, 2, 3, 3, 2, 2, 0, 5, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 7, 2, 2, 7, 5, 2, 3, 2, 2, 3, 5, 2, 3, 2, 5, 3, 2, 3, 7, 5, 2, 7, 2, 2, 3, 2, 2, 3, 2, 3, 3, 7, 3, 7, 5, 2, 7, 2, 5, 3, 2, 2, 7, 7, 3, 3, 2, 2, 7, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

For n > 8, a(12) = a(24) = 0.

The corresponding p: 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 7, 0, 11, 13, 7, 17, 19, 13, 23, 17, 19, 29, 31, 0, 11,... are not always the minimum values. The smallest primes p are in A223174.

Conjecture: except m = 25 and 49, all odd numbers > 17 are of the form m = p + 8*q where p and q are prime numbers.

LINKS

Michel Lagneau, Table of n, a(n) for n = 0..10000

EXAMPLE

a(14) = 2 because, for q=2 the corresponding p=13 and 13+8*2 = 29 is prime.

MAPLE

for n from 1 by 2 to 200 do:jj:=0:for j from 1 to 1000 while (jj=0) do:q:=ithprime(j):p:=n-8*q:if p> 0 and type(p, prime)=true  then jj:=1:printf(`%d, `, q):else fi:od:if jj=0 then printf(`%d, `, 0):else fi:od:

CROSSREFS

Cf. A219252, A219254, A219604, A219252, A223174, A103506.

Sequence in context: A036476 A104994 A118664 * A322213 A118205 A216265

Adjacent sequences:  A223172 A223173 A223174 * A223176 A223177 A223178

KEYWORD

nonn

AUTHOR

Michel Lagneau, May 09 2013

STATUS

approved

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Last modified October 27 23:26 EDT 2020. Contains 338047 sequences. (Running on oeis4.)