cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A181605 Twin primes ending in 7.

Original entry on oeis.org

7, 17, 107, 137, 197, 227, 347, 617, 827, 857, 1277, 1427, 1487, 1607, 1667, 1697, 1787, 1877, 1997, 2027, 2087, 2237, 2267, 2657, 2687, 3167, 3257, 3467, 3527, 3557, 3767, 3917, 4127, 4157, 4217, 4337, 4517, 4547, 4637, 4787, 4967, 5417, 5477, 5657
Offset: 1

Views

Author

Omar E. Pol, Nov 01 2010

Keywords

Comments

First disagrees with A092340 at n=26: A092340 contains 2707, but this sequence doesn't. Is this a subsequence of A092340? - Nathaniel Johnston, Jun 25 2011
Yes, it is a subsequence of A092340: see link. - Robert Israel, Apr 13 2021

Links

Crossrefs

Cf. A001097, A092340, A181603, A181604, A181606.

Programs

  • Maple
    [7, op(select(t -> isprime(t) and isprime(t+2), [seq(i,i=17..10000,30)]))]; # Robert Israel, Apr 13 2021
  • Mathematica
    Select[Prime@ Range@ 800, Mod[ #, 10] == 7 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)

Formula

A001097 INTERSECT A030432. - R. J. Mathar, Nov 03 2010

Extensions

More terms from R. J. Mathar and Robert G. Wilson v, Nov 03 2010

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

Views

Author

Martin Renner, Feb 11 2017

Keywords

Comments

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

Links

Crossrefs

Subset of A006512, A181603, A132230, A132243 and A132247.
Cf. A001359, A232880, A232881, A232882, A282321, A282322, A282323, A282324, A060229.

Programs

  • GAP
    Filtered(List([0..300], k -> 30*k+1), n -> IsPrime(n-2) and IsPrime(n));  # Muniru A Asiru, Mar 05 2018
  • Maple
    select(n -> isprime(n-2) and isprime(n), [seq(30*k+1, k=0..300)]); # Muniru A Asiru, Mar 05 2018
  • Mathematica
    1 + Select[30 Range@ 200, AllTrue[# + {-1, 1}, PrimeQ] &] (* Michael De Vlieger, Mar 26 2018 *)
  • PARI
    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

A181606 Twin primes ending in 9.

Original entry on oeis.org

19, 29, 59, 109, 139, 149, 179, 199, 229, 239, 269, 349, 419, 569, 599, 619, 659, 809, 829, 859, 1019, 1049, 1229, 1279, 1289, 1319, 1429, 1489, 1609, 1619, 1669, 1699, 1789, 1879, 1949, 1999, 2029, 2089, 2129, 2239, 2269, 2309, 2339, 2549, 2659, 2689
Offset: 1

Views

Author

Omar E. Pol, Nov 01 2010

Keywords

Links

Crossrefs

Cf. A001097, A181603, A181604, A181605.
Union of A060229 and A282324.

Programs

  • Maple
    filter:= proc(n)
  if not isprime(n) then return false fi;
  if n mod 3 = 1 then isprime(n-2) else isprime(n+2) fi
end proc:
select(filter, [seq(i,i=9..10^4,10)]); # Robert Israel, Nov 19 2023
  • Mathematica
    Select[Prime@ Range@ 800, Mod[ #, 10] == 9 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)
Select[Union[Flatten[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]]==2&]]],Mod[#,10]==9&] (* Harvey P. Dale, May 21 2024 *)

Extensions

More terms from Robert G. Wilson v, Nov 06 2010

A181604 Twin primes ending in 3.

Original entry on oeis.org

3, 13, 43, 73, 103, 193, 283, 313, 433, 463, 523, 643, 823, 883, 1033, 1063, 1093, 1153, 1303, 1453, 1483, 1723, 1873, 1933, 2083, 2113, 2143, 2383, 2593, 2713, 2803, 3253, 3373, 3463, 3583, 3673, 3823, 3853, 4003, 4093, 4243, 4273, 4423, 4483, 4723, 4933
Offset: 1

Views

Author

Omar E. Pol, Nov 01 2010

Keywords

Links

Crossrefs

Cf. A001097, A181603, A181605, A181606.

Programs

  • Maple
    isA181604 := proc(p)
    if isprime(p) and (isprime(p-2) or isprime(p+2)) then
        if modp(p,10) = 3 then
            true;
        else
            false;
        end if ;
    else
        false;
    end if;
end proc: # R. J. Mathar, Feb 14 2017
  • Mathematica
    Select[Prime@Range@700, Mod[ #, 10] == 3 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)

Extensions

More terms from Robert G. Wilson v, Nov 06 2010

A248367 Initial members of prime quadruples (n, n+2, n+36, n+38).

Original entry on oeis.org

5, 71, 101, 191, 311, 821, 1451, 4091, 4481, 4931, 5441, 6791, 12071, 13721, 14591, 17921, 18251, 20441, 20771, 20981, 21521, 21611, 35801, 38711, 41141, 41981, 43541, 46271, 47351, 47741, 48821, 49331, 53231, 64151, 70841
Offset: 1

Views

Author

Karl V. Keller, Jr., Jan 11 2015

Keywords

Comments

This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+36,n+38).
This sequence is a subsequence of A001359 (lesser of twin primes).
Excluding 5, this sequence is a subsequence of A132232 (primes, 11 mod 30).

Examples

			For n=71, the numbers 71, 73, 107, 109, are primes.

Links

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A181603 (twin primes, end 1).

Programs

  • Mathematica
    a248367[n_] := Select[Prime@Range@n, And[PrimeQ[# + 2], PrimeQ[# + 36], PrimeQ[# + 38]] &]; a248367[8000] (* Michael De Vlieger, Jan 11 2015 *)
Select[Prime[Range[8000]],AllTrue[#+{2,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 17 2019 *)
  • Python
    from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+36) and isprime(n+38): print(n,end=', ')

A247089 Initial members of prime quadruples (p, p+2, p+30, p+32).

Original entry on oeis.org

11, 29, 41, 71, 107, 149, 197, 239, 281, 431, 569, 827, 1019, 1031, 1061, 1289, 1451, 1667, 1997, 2081, 2111, 2237, 2309, 2657, 2969, 3299, 3329, 3359, 3527, 3821, 4019, 4127, 4229, 4241, 4517, 5849, 6269, 6659, 6761, 7457, 7559, 8597
Offset: 1

Views

Author

Karl V. Keller, Jr., Jan 10 2015

Keywords

Comments

Primes p such that (p, p+2) and (p+30, p+32) are twin prime pairs.
This sequence is a subsequence of A001359 (lesser of twin primes).
The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).
The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).
The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).

Examples

			For n=11, the numbers 11, 13, 41, 43, are primes.

Links

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).

Programs

  • Mathematica
    a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* Michael De Vlieger, Jan 11 2015 *)
  • Python
    from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+30) and isprime(n+32): print(n,end=', ')
Showing 1-6 of 6 results.

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