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A060229 Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30. 17
29, 59, 149, 179, 239, 269, 419, 569, 599, 659, 809, 1019, 1049, 1229, 1289, 1319, 1619, 1949, 2129, 2309, 2339, 2549, 2729, 2789, 2969, 2999, 3119, 3299, 3329, 3359, 3389, 3539, 3929, 4019, 4049, 4229, 4259, 4649, 4799, 5009, 5099, 5279, 5519, 5639 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, smaller of twin prime pair with primes in different decades.

Primes p such that p and p+2 are prime factors of Fibonacci(p-1) and Fibonacci(p+1) respectively. - Michel Lagneau, Jul 13 2016

The union of this sequence and A282326 gives A132243. - Martin Renner, Feb 11 2017

The union of {3,5}, A282321, A282323 and this sequence gives A001359. - Martin Renner, Feb 11 2017

The union of {3,5,7}, A282321, A282322, A282323, A282324, this sequence and A282326 gives A001097. - Martin Renner, Feb 11 2017

Number of terms less than 10^k, k=2,3,4,...: 2, 11, 72, 407, 2697, 19507, 146516, ... - Muniru A Asiru, Jan 29 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..1000

EXAMPLE

For the pair {149,151} (149 + 151)/2 = 5*30.

MAPLE

isA060229 := proc(n)

    if modp(n+1, 30) =0 and isprime(n) and isprime(n+2) then

        true;

    else

        false;

    end if;

end proc:

A060229 := proc(n)

    option remember;

    if n =1 then

        29;

    else

        for a from procname(n-1)+2 by 2 do

            if isA060229(a) then

                return a;

            end if;

        end do:

    end if;

end proc:

seq(A060229(n), n=1..80) ; # R. J. Mathar, Feb 19 2017

MATHEMATICA

Select[Prime@ Range[10^3], PrimeQ[# + 2] && Mod[# + 1, 30] == 0 &] (* Michael De Vlieger, Jul 14 2016 *)

PROG

(PARI) isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 30); \\ Michel Marcus, Dec 11 2013

(MAGMA) [p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 29 ]; // Vincenzo Librandi, Feb 13 2017

(GAP) Filtered(List([0..200], k -> 30*k-1), n -> IsPrime(n) and IsPrime(n+2));  # Muniru A Asiru, Feb 02 2018

CROSSREFS

Cf. A001359, A002110, A060230, A060231, A158277, A158861.

Subset of A001097, A001359, A132236, A132243 and A132247.

Sequence in context: A042672 A042670 A129813 * A326897 A139507 A196940

Adjacent sequences:  A060226 A060227 A060228 * A060230 A060231 A060232

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 21 2001

EXTENSIONS

Minor edits by Ray Chandler, Apr 02 2009

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)