A185398 a(n) is the number of odd primes p < prime(n)^2 such that prime(n)# - p is prime.

0, 1, 6, 9, 15, 14, 21, 24, 22, 43, 38, 50, 54, 43, 61, 62, 74, 66, 79, 81, 87, 94, 93, 99, 101, 101, 110, 114, 119, 123, 129, 136, 160, 150, 184, 158, 178, 196, 171, 176, 180, 190, 201, 202, 222, 221, 230, 252, 242, 244, 251, 235, 261, 262

Offset

1,3

Comments

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

Links

Pierre CAMI, Table of n, a(n) for n = 1..176

Example

prime(1)#=2 , a(n)=0 ( no solution )
prime(2)#=6 , 6-3=3 prime , a(1)=1
prime(3)#=30, 30-7=23,30-11=19,30-13=17,30-17=13,30-19=11,30-23=7
so a(3)=6

Prog

(PFGW Scriptify) SCRIPT
DIM nn, 1
DIM kk
DIM cc
DIM dd
DIMS tt
DIMS ss
OPENFILEOUT myout, res
LABEL loopn
SET nn, nn+1
SET kk, nn
SET cc, 0
SET dd, 0
LABEL loopk
SET kk, kk+1
IF p(kk)>p(nn)^2 THEN GOTO a
SETS tt, %d, %d, %d\,; nn; p(nn); -p(kk)
PRP p(nn)#-p(kk), tt
IF ISPRIME THEN SET cc, cc+1
IF ISPRP THEN SET cc, cc+1
SETS tt, %d, %d, %d\,; nn; p(nn); p(kk)
PRP p(nn)#+p(kk), tt
IF ISPRIME THEN SET dd, dd+1
IF ISPRP THEN SET dd, dd+1
GOTO loopk
LABEL a
SETS ss, %d, %d, %d\,; nn; cc; dd
WRITE myout, ss
GOTO loopn
(PARI) a(n)=my(P=prod(k=1, n, prime(k)), s=0); forprime(p=2, prime(n)^2, s+=ispseudoprime(P-p)); s

Crossrefs

Cf. A186413.

Sequence in context: A303162 A242042 A316021 * A316022 A316023 A139322

Adjacent sequences: A185395 A185396 A185397 * A185399 A185400 A185401

Keyword

nonn

Author

Pierre CAMI, Feb 21 2011

Extensions

Edited by Charles R Greathouse IV, Feb 21 2011

Status

approved