A235649 Define a(4)=3 then a(n+1)is the smallest prime P such that a(n)<=P< n with 2*n-P=Q prime and if not possible a(n+1) is the smallest prime P such that P<a(n)<n with 2*n-P=Q prime

3, 3, 5, 3, 3, 5, 7, 3, 5, 7, 11, 11, 13, 3, 5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 3, 5, 7, 19, 23, 23, 31, 3, 5, 7, 17, 17, 19, 23, 23, 3, 5, 7, 13, 23, 23, 31, 41, 41, 43, 47, 47, 3, 3, 5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 31, 47, 59, 61, 3, 5, 7, 11

Offset

4,1

Links

Pierre CAMI, Table of n, a(n) for n = 4..10005

Example

a(4)=3 as 2*4-3=5 prime by definition
a(5)=3 as 2*5-3=7 prime, a(5)=a(4), a(5)<5
a(6)=5 as 2*6-5=7 prime, a(6)>a(5), a(6)<6
a(7)=5 not possible as 14-5=9 composite
a(7)=7 not possible as 7=7
a(7)=3 as 2*7-3=11 prime
a(8)=3 as 2*8-3=13 prime

Prog

(PFGW & SCRIPT)
SCRIPT
DIM n, 3
DIM i
DIM pp
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
OPENFILEIN maf, prime.txt
GETNEXT i, maf
GETNEXT i, maf
LABEL a
SET n, n+1
IF n>10005 THEN END
SET pp, 2*n-i
SETS t, %d, %d\,; n; i
PRP pp, t
IF ISPRP THEN GOTO c
LABEL b
GETNEXT i, maf
IF n-i<3 THEN GOTO d
SET pp, 2*n-i
SETS t, %d, %d\,; n; i
PRP pp, t
IF ISPRP THEN GOTO c
GOTO b
LABEL c
WRITE myf, t
GOTO a
LABEL d
CLOSEFILE maf
SET n, n-1
GOTO loop1

Crossrefs

Cf. A002373, A020483

Sequence in context: A136019 A242017 A063714 * A113965 A162277 A365512

Adjacent sequences: A235646 A235647 A235648 * A235650 A235651 A235652

Keyword

nonn

Author

Pierre CAMI, Jan 13 2014

Status

approved