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A228968 Prime p such that p and p+2 are twin primes and p^2+p-1 p^2+p+1 are also twin primes. 4
3, 5, 41, 59, 101, 2729, 3251, 9719, 11549, 12251, 19211, 28619, 41201, 47711, 49391, 55439, 58229, 61979, 63029, 63311, 79631, 81371, 85331, 103391, 122039, 135719, 153509, 157349, 164249, 167441, 178601, 188861, 197711, 208001, 209819, 216779, 219311, 226451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A088483.

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..10000

EXAMPLE

3 and 5 twin primes as 3*3+3-1=11 and 13, a(2)=3.

5 and 7 twin primes as 5*5+5-1=29 and 31, a(3)=5.

MATHEMATICA

Select[Transpose[Select[Partition[Prime[Range[21000]], 2, 1], #[[2]]-#[[1]] == 2&]][[1]], AllTrue[#^2+#+{1, -1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 10 2014 *)

PROG

PFGW & SCRIPTIFY

SCRIPT

DIM n, 0

DIM m

DIM k, 0

DIMS ta

OPENFILEOUT myf, a(n).txt

OPENFILEIN maf, twin.txt

LABEL loop1

SET n, n+1

IF n>2999999 THEN END

GETNEXT m, maf

SETS ta, %d\,; n

PRP m^2+m-1, ta

IF ISPRP THEN GOTO a

GOTO loop1

LABEL a

PRP m^2+m+1, ta

IF ISPRP THEN GOTO b

GOTO loop1

LABEL b

WRITE myf, m

GOTO loop1

The file twin.txt has the first 3000000 of first of twin primes

(PFGW) ABC2 $a & $a+2 & $a^2+$a-1 & $a^2+$a+1

a: 1 to 3000000

Charles R Greathouse IV, Sep 10 2013

(PARI) is(n)=isprime(n)&&isprime(n+2)&&isprime(n^2+n-1)&&isprime(n^2+n+1) \\ Charles R Greathouse IV, Sep 10 2013

(Sage)

[x for x in primes_first_n(900) if x+2 in Primes() and x^2+x-1 in Primes() and x^2+x+1 in Primes()] #Tom Edgar, Sep 10 2013

CROSSREFS

Cf. A088483.

Sequence in context: A176112 A215133 A146318 * A178545 A145912 A096058

Adjacent sequences:  A228965 A228966 A228967 * A228969 A228970 A228971

KEYWORD

nonn

AUTHOR

Pierre CAMI, Sep 10 2013

STATUS

approved

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Last modified August 14 22:45 EDT 2022. Contains 356122 sequences. (Running on oeis4.)