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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 December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)