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A237885 a(n) is the number of ways that 4n can be written as p+q (p>q) with p, q, (p-q)/2, 4n-(p-q)/2 all prime numbers. 1
0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 4, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 5, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 3, 0, 0, 2, 0, 1, 3, 0, 0, 3, 1, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

2n=q+(p-q)/2; 6n=p+(4n-(p-q)/2).

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

EXAMPLE

When n=4, 4n=16, 16=13+3, (13-3)/2=5, 16-5=11, all four numbers {3, 5, 11, 13} are prime numbers.  There is no other such four number set with this property, so a(4)=1;

When n=30, 4n=120.

  120=113+7, (113-7)/2=53, 120-53=67.  Set 1: {7, 53, 67, 113}.

  120=109+11, (109-11)/2=49=7*7, X

  120=107+13, (107-13)/2=47, 120-47=73. Set 2: {13, 47, 73, 107}.

  120=103+17, (103-17)/2=43, 120-43=77=7*11, X

  120=101+19, (101-19)/2=41, 120-41=79. Set 3: {19, 41, 79, 101}.

  120=97+23, (97-23)/2=37, 120-37=83. Set 4: {23, 37, 83, 97}.

  120=89+31, (89-31)/2=29, 120-29=91=7*13, X

  120=83+37, same with Set 4.

  120=79+41, same with Set 3.

  120=73+47, same with Set 2.

  120=67+53, same with Set 1.

  120=61+59, (61-59)/2=1, X

  So four acceptable sets have been found, and therefore a(30)=4.

MATHEMATICA

Table[qn = 4*n; p = 2*n - 1; ct = 0; While[p = NextPrime[p]; p < qn, q = qn - p; If[PrimeQ[q] && PrimeQ[(p - q)/2] && PrimeQ[qn - (p - q)/2], ct++]]; ct/2, {n, 1, 87}]4*n-1

PROG

(PARI) a(n)=my(s); forprime(p=2, n, if(isprime(2*n-p) && isprime(2*n+p) && isprime(4*n-p), s++)); s \\ Charles R Greathouse IV, Mar 15 2015

CROSSREFS

Cf. A002375.

Sequence in context: A002284 A016424 A108913 * A139032 A182035 A095808

Adjacent sequences:  A237882 A237883 A237884 * A237886 A237887 A237888

KEYWORD

nonn,easy

AUTHOR

Lei Zhou, Feb 14 2014

STATUS

approved

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Last modified October 18 16:17 EDT 2018. Contains 316323 sequences. (Running on oeis4.)