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A235859 Define a(4)=3, then a(n+1) is the smallest prime P such that a(n) <= P < 2*n with 2*n-P=Q prime and, if not possible, a(n+1) is the smallest prime P such that P < a(n) < 2*n with 2*n-P=Q prime. 1
3, 3, 5, 11, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 47, 47, 53, 53, 53, 59, 59, 59, 61, 67, 67, 67, 71, 71, 73, 79, 79, 79, 83, 83, 89, 89, 89, 19, 29, 29, 31, 47, 47, 67, 71, 71, 73, 89, 89, 103, 107, 107, 109, 113, 113 (list; graph; refs; listen; history; text; internal format)
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)=11 as 2*7-11=3 prime

.........................

a(48)=89 as 2*48-89=7 prime

a(49)=89 not possible as 2*49-89=9 composite

a(49)=97 not possible as 2*49-97=unity

a(49)=19 as 19 is the smallest prime such that 2*49-19 is prime

a(50)=29 as 29 is the smallest prime >=19 such that 2*50-29 is 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 i==n THEN GOTO b

IF 2*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, A235649.

Sequence in context: A132751 A218354 A286514 * A279790 A338847 A032020

Adjacent sequences:  A235856 A235857 A235858 * A235860 A235861 A235862

KEYWORD

nonn,less

AUTHOR

Pierre CAMI, Jan 16 2014

STATUS

approved

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Last modified September 21 00:14 EDT 2021. Contains 347596 sequences. (Running on oeis4.)