A132243 -id:A132243 - cp's OEIS frontend

A060229 Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.

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

Offset: 1

Labos Elemer, Mar 21 2001

nonn

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

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

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

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

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

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

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

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

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

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

Minor edits by Ray Chandler, Apr 02 2009

A282326 Greater of twin primes congruent to 1 (mod 30).

Original entry on oeis.org

31, 61, 151, 181, 241, 271, 421, 571, 601, 661, 811, 1021, 1051, 1231, 1291, 1321, 1621, 1951, 2131, 2311, 2341, 2551, 2731, 2791, 2971, 3001, 3121, 3301, 3331, 3361, 3391, 3541, 3931, 4021, 4051, 4231, 4261, 4651, 4801, 5011, 5101, 5281, 5521, 5641, 5851

Offset: 1

Martin Renner, Feb 11 2017

nonn

The union of [A060229 and this sequence] is A132243.
The union of [{5, 7}, A282322, A282324 and this sequence] is the greater of twin primes sequence A006512.
The union of [{3, 5, 7}, A282321 to A060229 and this sequence] is the twin primes sequence A001097.
Number of terms less than 10^k, k=2,3,4,...: 2, 11, 72, 407, 2697, 19507, 146516, ... - Muniru A Asiru, Mar 05 2018

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Subset of A006512, A181603, A132230, A132243 and A132247.

Cf. A001359, A232880, A232881, A232882, A282321, A282322, A282323, A282324, A060229.

Filtered(List([0..300], k -> 30*k+1), n -> IsPrime(n-2) and IsPrime(n));  # Muniru A Asiru, Mar 05 2018

select(n -> isprime(n-2) and isprime(n), [seq(30*k+1, k=0..300)]); # Muniru A Asiru, Mar 05 2018

1 + Select[30 Range@ 200, AllTrue[# + {-1, 1}, PrimeQ] &] (* Michael De Vlieger, Mar 26 2018 *)

list(lim)=my(v=List(),p=2); forprime(q=3,lim, if(q-p==2 && q%30==1, listput(v,q)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017

A132242 Twin primes congruent to {17, 19} mod 30.

Original entry on oeis.org

17, 19, 107, 109, 137, 139, 197, 199, 227, 229, 347, 349, 617, 619, 827, 829, 857, 859, 1277, 1279, 1427, 1429, 1487, 1489, 1607, 1609, 1667, 1669, 1697, 1699, 1787, 1789, 1877, 1879, 1997, 1999, 2027, 2029, 2087, 2089, 2237, 2239, 2267, 2269, 2657, 2659

Offset: 1

Omar E. Pol, Aug 15 2007

Roger L. Bagula, Table of n, a(n) for n = 1..130
C. K. Caldwell, The Prime Pages.
C. K. Caldwell, Twin Primes.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001097, A001359, A006512, A039949.

Cf. A132243, A132241.

a[0] = 7; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 2], {a[n],a[n] + 2}, {}], {n, 0, 1000}]] (* Roger L. Bagula, May 04 2008 *)

More terms from Roger L. Bagula, May 04 2008

A076746 List giving pairs of primes of the form 10k+3 and 10k+7.

Original entry on oeis.org

3, 7, 13, 17, 43, 47, 103, 107, 163, 167, 193, 197, 223, 227, 313, 317, 463, 467, 613, 617, 643, 647, 673, 677, 823, 827, 853, 857, 883, 887, 1093, 1097, 1213, 1217, 1303, 1307, 1423, 1427, 1483, 1487, 1663, 1667, 1693, 1697, 1783, 1787, 1873, 1877, 1993

Offset: 1

Cino Hilliard, Nov 11 2002

nonn

Except for 3 and 7, all pairs are 30k+13 and 30k+17.

Is this sequence infinite?

			43 and 47 are in the sequence because both are prime; 73 and 77 aren't because not both are primes.

Roger L. Bagula, May 04 2008, Table of n, a(n) for n = 1..142

Cf. A001097.

Cf. A132243, A132242.

&cat[[10*k+3, 10*k+7]: k in [0..250]| IsPrime(10*k+3) and IsPrime(10*k+7)]; // Vincenzo Librandi, Jun 17 2016

a[0] = 3; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 4], {a[n],a[n] + 4}, {}], {n, 0, 1000}]] (* Roger L. Bagula, May 04 2008 *)
Flatten[Select[Table[10n+{3,7},{n,0,200}],And@@PrimeQ[#]&]] (* Harvey P. Dale, Dec 31 2013 *)

forstep(x=3,2000,10, if(isprime(x) && isprime(x+4), print1(x, ", ", x+4, ", ")))

Edited by Don Reble, Jun 07 2003

More terms from Roger L. Bagula, May 04 2008

A138122 Cousin primes, the lower of which is 7 (mod 10).

Original entry on oeis.org

7, 11, 37, 41, 67, 71, 97, 101, 127, 131, 277, 281, 307, 311, 397, 401, 457, 461, 487, 491, 757, 761, 877, 881, 907, 911, 937, 941, 967, 971, 1087, 1091, 1297, 1301, 1447, 1451, 1567, 1571, 1597, 1601, 1867, 1871, 2137, 2141, 2347, 2351, 2377, 2381, 2437

Offset: 1

Roger L. Bagula, May 04 2008

nonn

Start from the intersection of A023200 and A030432, then add the associated members of A046132. The last digits are obviously periodic as A010688. - R. J. Mathar, Nov 26 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A132243, A132242, A076746.

a[0] = 7; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 4], {a[n],a[n] + 4}, {}], {n, 0, 1000}]]

Replaced Mathematica definition by humanly readable phrase. - R. J. Mathar, Nov 26 2008

cp's OEIS Frontend

A060229 Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.

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A282326 Greater of twin primes congruent to 1 (mod 30).

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A132242 Twin primes congruent to {17, 19} mod 30.

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A076746 List giving pairs of primes of the form 10k+3 and 10k+7.

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Programs

Magma

Mathematica

PARI

Extensions

A138122 Cousin primes, the lower of which is 7 (mod 10).

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions