A185398 - OEIS

%I #17 May 13 2013 01:49:30

%S 0,1,6,9,15,14,21,24,22,43,38,50,54,43,61,62,74,66,79,81,87,94,93,99,

%T 101,101,110,114,119,123,129,136,160,150,184,158,178,196,171,176,180,

%U 190,201,202,222,221,230,252,242,244,251,235,261,262

%N a(n) is the number of odd primes p < prime(n)^2 such that prime(n)# - p is prime.

%C a(n) is not so far from prime(n).

%H Pierre CAMI, <a href="/A185398/b185398.txt">Table of n, a(n) for n = 1..176</a>

%e prime(1)#=2 , a(n)=0 ( no solution )

%e prime(2)#=6 , 6-3=3 prime , a(1)=1

%e prime(3)#=30, 30-7=23,30-11=19,30-13=17,30-17=13,30-19=11,30-23=7

%e so a(3)=6

%o (PFGW Scriptify) SCRIPT

%o DIM nn,1

%o DIM kk

%o DIM cc

%o DIM dd

%o DIMS tt

%o DIMS ss

%o OPENFILEOUT myout,res

%o LABEL loopn

%o SET nn,nn+1

%o SET kk,nn

%o SET cc,0

%o SET dd,0

%o LABEL loopk

%o SET kk,kk+1

%o IF p(kk)>p(nn)^2 THEN GOTO a

%o SETS tt,%d,%d,%d\,;nn;p(nn);-p(kk)

%o PRP p(nn)#-p(kk),tt

%o IF ISPRIME THEN SET cc,cc+1

%o IF ISPRP THEN SET cc,cc+1

%o SETS tt,%d,%d,%d\,;nn;p(nn);p(kk)

%o PRP p(nn)#+p(kk),tt

%o IF ISPRIME THEN SET dd,dd+1

%o IF ISPRP THEN SET dd,dd+1

%o GOTO loopk

%o LABEL a

%o SETS ss,%d,%d,%d\,;nn;cc;dd

%o WRITE myout,ss

%o GOTO loopn

%o (PARI) a(n)=my(P=prod(k=1,n,prime(k)),s=0); forprime(p=2,prime(n)^2, s+=ispseudoprime(P-p));s

%Y Cf. A186413.

%K nonn

%O 1,3

%A _Pierre CAMI_, Feb 21 2011

%E Edited by _Charles R Greathouse IV_, Feb 21 2011