A156311 Number of ways to write prime(n) = prime(k) + prime(k+1)*m.

0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 1, 1, 3, 2, 1, 1, 0, 1, 2, 0, 2, 3, 0, 1, 2, 1, 0, 2, 1, 3, 2, 2, 2, 0, 1, 1, 2, 3, 2, 1, 1, 2, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 1, 3, 1, 1, 4, 3, 1, 1, 3, 2, 0, 1, 1, 1, 3, 3, 1, 1, 0, 3, 3, 2, 4, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1, 3, 2, 3, 1, 2, 0, 2, 3, 1, 3, 1, 2, 5, 3, 1, 1

Offset

1,9

Comments

a(n) = #{k: prime(n) mod prime(k+1) = prime(k)};

a(A049084(A156312(n)))>0; a(A049084(A156313(n)))=0;

a(A049084(A156314(n)))=n and a(m)<n for m < A049084(A156314(n)).

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Example

A000040(14)=43: a(14) = #{3+5*8} = 1;
A000040(15)=47: a(15) = #{2+3*15, 5+7*6, 13+17*2} = 3;
A000040(16)=53: a(16) = #{2+3*17, 3+5*10} = 2.

Prog

(PARI) a(n, t=prime(n))=my(s, p=2); forprime(q=3, nextprime(t/2), if(t%q==p, s++); p=q); s \\ Charles R Greathouse IV, Mar 13 2015

Crossrefs

Sequence in context: A376629 A206442 A137581 * A270740 A189463 A287451

Adjacent sequences: A156308 A156309 A156310 * A156312 A156313 A156314

Keyword

nonn

Author

Reinhard Zumkeller, Feb 07 2009

Status

approved