A153418 -id:A153418 - cp's OEIS frontend

A031936 Lower prime of a difference of 18 between consecutive primes.

523, 1069, 1259, 1381, 1759, 1913, 2161, 2503, 2861, 3803, 3889, 4159, 4373, 4423, 4463, 4603, 4703, 4733, 5059, 5209, 5483, 6011, 6229, 6451, 6529, 6581, 6619, 7159, 7351, 7393, 7433, 7459, 7621, 7883, 8191, 8761, 9109, 9293, 9749

Offset: 1

Jeff Burch

nonn

Subsequence of A153418: a(1)=523=A153418(46), a(2)=1069=A153418(80), etc. - Zak Seidov, Sep 13 2015

No terms are congruent to 7 mod 10. - Michel Marcus, Sep 14 2015

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for primes, gaps between

Cf. A153418.

[p: p in PrimesUpTo(10000) | NextPrime(p)-p eq 18]; // Bruno Berselli, Apr 09 2013

Transpose[Select[Partition[Prime[Range[1300]], 2, 1], Last[#] - First[#] == 18 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

isok(p) = isprime(p) && (nextprime(p+1) == p+18); \\ Michel Marcus, Sep 14 2015

a(n) = prime(A320707(n)). - R. J. Mathar, Apr 30 2024

A156104 Primes p such that p+36 is also prime.

Original entry on oeis.org

5, 7, 11, 17, 23, 31, 37, 43, 47, 53, 61, 67, 71, 73, 101, 103, 113, 127, 131, 137, 157, 163, 191, 193, 197, 227, 233, 241, 257, 271, 277, 281, 311, 313, 317, 331, 337, 347, 353, 373, 383, 397, 421, 431, 443, 463, 467, 487, 521, 541, 557, 563, 571, 577, 607

Offset: 1

Vincenzo Librandi, Feb 08 2009

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

Cf. A156112.

Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), A252089 (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), this sequence (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

[p: p in PrimesUpTo(1000) | IsPrime(p + 36)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[1000]], PrimeQ[(#+ 36)]&] (* Vincenzo Librandi, Oct 31 2012 *)

A153419 Primes p such that p+20 is also prime.

Original entry on oeis.org

3, 11, 17, 23, 41, 47, 53, 59, 83, 89, 107, 131, 137, 173, 179, 191, 251, 257, 263, 293, 311, 317, 347, 353, 359, 389, 401, 419, 443, 467, 479, 503, 521, 557, 587, 593, 599, 641, 653, 719, 809, 839, 857, 863, 887, 947, 971, 977, 1013, 1019, 1031, 1049, 1097

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

			3 is in the sequence because 3+20=23 is prime; 11 is in the sequence because 11+20=31 is prime.

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Cf. A153417, A049488, A153418.

[p: p in PrimesUpTo(1100) | IsPrime(p + 20)]; // Vincenzo Librandi, Apr 14 2013

for a from 1 to 140 do if isprime(a) and isprime(a+20) then print(a)
  end if;  end do; # Matt C. Anderson, Jun 20 2022

Select[Prime[Range[200]], PrimeQ[(# + 20)]&] (* Vincenzo Librandi, Apr 14 2013 *)

Definition improved from Bruno Berselli, Oct 31 2012

A252089 Primes p such that p + 26 is prime.

Original entry on oeis.org

3, 5, 11, 17, 41, 47, 53, 71, 83, 101, 113, 131, 137, 167, 173, 197, 251, 257, 281, 311, 347, 353, 383, 431, 461, 521, 587, 593, 617, 647, 683, 701, 743, 761, 797, 827, 857, 881, 911, 941, 971, 983, 1013, 1061, 1091, 1097, 1103, 1187, 1223, 1277, 1301, 1373

Offset: 1

Vincenzo Librandi, Dec 14 2014

			17 is in this sequence because 17+26 = 43 is prime.
431 is in this sequence because 431+26 = 457 is prime.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. sequences of the type p+n are primes: A001359 (n=2), A023200 (n=4), A023201 (n=6), A023202 (n=8), A023203 (n=10), A046133 (n=12), A153417 (n=14), A049488 (n=16), A153418 (n=18), A153419 (n=20), A242476 (n=22), A033560 (n=24), this sequence (n=26), A252090 (n=28), A049481 (n=30), A049489 (n=32), A252091 (n=34), A156104 (n=36); A062284 (n=50), A049490 (n=64), A156105 (n=72), A156107 (n=144).

[NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+26)];

Select[Prime[Range[200]], PrimeQ[# + 26] &]

A156328 List of prime pairs of the form (p, p+18).

Original entry on oeis.org

5, 23, 11, 29, 13, 31, 19, 37, 23, 41, 29, 47, 41, 59, 43, 61, 53, 71, 61, 79, 71, 89, 79, 97, 83, 101, 89, 107, 109, 127, 113, 131, 131, 149, 139, 157, 149, 167, 163, 181, 173, 191, 179, 197, 181, 199, 193, 211, 211, 229, 223, 241, 233, 251, 239, 257, 251, 269, 263

Offset: 1

Vincenzo Librandi, Feb 08 2009

The two primes p and p+18 are not necessarily adjacent.

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

Cf. A153418.

Flatten[Select[{#, # + 18} &/@Prime[Range[1000]], PrimeQ[Last[#]]&]] (* Vincenzo Librandi, Nov 01 2012 *)

A161723 Middle members p of prime triples (p-18,p,p+18).

Original entry on oeis.org

23, 29, 41, 61, 71, 79, 89, 131, 149, 181, 211, 251, 331, 349, 401, 439, 449, 461, 659, 691, 701, 709, 751, 769, 839, 929, 1031, 1051, 1069, 1231, 1301, 1471, 1549, 1601, 1619, 1741, 1759, 1889, 1931, 2011, 2081, 2161, 2221, 2269, 2399, 2441, 2459, 2521

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 17 2009

nonn

The three primes p-18, p and p+18 are not necessarily consecutive.

			23 is the middle in the triple of three primes (23-18=5, 23, 23+18=41) with arithmetic progression 18.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A006489, A137796.

q=6*3; lst={}; Do[p=Prime[n]; If[PrimeQ[p-q] && PrimeQ[p+q], AppendTo[lst,p]], {n, 5000}]; lst
Select[Prime[Range[7,400]],AllTrue[#+{18,-18},PrimeQ]&] (* Harvey P. Dale, Apr 21 2024 *)

{p: p in A153418 and p-18 in A153418} - R. J. Mathar, Sep 22 2009

Rephrased the definition - R. J. Mathar, Sep 22 2009

A231608 Table whose n-th row consists of primes p such that p + 2n is also prime, read by antidiagonals.

Original entry on oeis.org

3, 3, 5, 5, 7, 11, 3, 7, 13, 17, 3, 5, 11, 19, 29, 5, 7, 11, 13, 37, 41, 3, 7, 13, 23, 17, 43, 59, 3, 5, 11, 19, 29, 23, 67, 71, 5, 7, 17, 17, 31, 53, 31, 79, 101, 3, 11, 13, 23, 19, 37, 59, 37, 97, 107, 7, 11, 13, 31, 29, 29, 43, 71, 41, 103, 137

Offset: 1

T. D. Noe, Nov 26 2013

			The following sequences are read by antidiagonals
{3, 5, 11, 17, 29, 41, 59, 71, 101, 107,...}
{3, 7, 13, 19, 37, 43, 67, 79, 97, 103,...}
{5, 7, 11, 13, 17, 23, 31, 37, 41, 47,...}
{3, 5, 11, 23, 29, 53, 59, 71, 89, 101,...}
{3, 7, 13, 19, 31, 37, 43, 61, 73, 79,...}
{5, 7, 11, 17, 19, 29, 31, 41, 47, 59,...}
{3, 5, 17, 23, 29, 47, 53, 59, 83, 89,...}
{3, 7, 13, 31, 37, 43, 67, 73, 97, 151,...}
{5, 11, 13, 19, 23, 29, 41, 43, 53, 61,...}
{3, 11, 17, 23, 41, 47, 53, 59, 83, 89,...}
...

T. D. Noe, Rows n = 1..100 of triangle, flattened

Cf. A001359, A023200, A023201, A023202, A023203.
Cf. A046133, A153417, A049488, A153418, A153419.
Cf. A020483 (numbers in first column).
Cf. A086505 (numbers on the diagonal).

A231608 := proc(n,k)
    local j,p ;
    j := 0 ;
    p := 2;
    while j < k do
        if isprime(p+2*n ) then
            j := j+1 ;
        end if;
        if j = k then
            return p;
        end if;
        p := nextprime(p) ;
    end do:
end proc:
for n from 1 to 10 do
    for k from 1 to 10 do
        printf("%3d ",A231608(n,k)) ;
    end do;
    printf("\n") ;
end do: # R. J. Mathar, Nov 19 2014

nn = 10; t = Table[Select[Range[100*nn], PrimeQ[#] && PrimeQ[# + 2*n] &, nn], {n, nn}]; Table[t[[n-j+1, j]], {n, nn}, {j, n}]

A156109 Primes p such that p+18 and p+36 are both prime.

Original entry on oeis.org

5, 11, 23, 43, 53, 61, 71, 113, 131, 163, 193, 233, 313, 331, 383, 421, 431, 443, 641, 673, 683, 691, 733, 751, 821, 911, 1013, 1033, 1051, 1213, 1283, 1453, 1531, 1583, 1601, 1723, 1741, 1871, 1913, 1993, 2063, 2143, 2203, 2251, 2381, 2423, 2441, 2503

Offset: 1

Vincenzo Librandi, Feb 08 2009

A153418 INTERSECT A156104. [Bruno Berselli, Nov 01 2012]

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

Cf. A153418, A156104.

[p: p in PrimesUpTo(3000)|IsPrime(p + 18) and IsPrime (p + 36)]; // Vincenzo Librandi, Oct 31 2012

a := proc (n) if isprime(ithprime(n)+18) = true and isprime(ithprime(n)+36) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 400); # Emeric Deutsch, Mar 02 2009

Select[Prime[Range[3000]], And @@ PrimeQ[{# + 18, # + 36}]&] (* Vincenzo Librandi, Oct 31 2012 *)

More terms from Emeric Deutsch, Mar 02 2009

A156110 Primes p such that p+18 and p+72 are both prime.

Original entry on oeis.org

11, 29, 41, 79, 109, 139, 179, 211, 239, 349, 431, 449, 491, 569, 601, 701, 739, 751, 809, 811, 839, 911, 919, 991, 1021, 1031, 1051, 1091, 1231, 1289, 1301, 1381, 1409, 1471, 1481, 1549, 1759, 1861, 1931, 2011, 2069, 2081, 2221, 2269, 2339, 2459, 2521

Offset: 1

Vincenzo Librandi, Feb 08 2009

A153418 INTERSECT A156105. [Bruno Berselli, Nov 01 2012]

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

Cf. A153418, A156105.

[p: p in PrimesUpTo(3000)|IsPrime(p + 18) and IsPrime (p + 72)]; // Vincenzo Librandi, Oct 31 2012

Select[Prime[Range[3000]], And @@ PrimeQ[{# + 18, # + 72}]&] (* Vincenzo Librandi, Oct 31 2012 *)

A156111 Primes p such that p+18 and p+144 are both prime.

Original entry on oeis.org

5, 13, 19, 23, 29, 53, 79, 83, 89, 113, 139, 149, 163, 173, 193, 223, 239, 313, 379, 443, 449, 503, 599, 613, 643, 683, 709, 733, 739, 743, 809, 839, 919, 953, 1069, 1153, 1163, 1279, 1283, 1289, 1303, 1409, 1453, 1493, 1549, 1553, 1579, 1609, 1723, 1993, 1999

Offset: 1

Vincenzo Librandi, Feb 08 2009

A153418 INTERSECT A156107. [Bruno Berselli, Nov 01 2012]

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

Cf. A153418, A156107.

[p: p in PrimesUpTo(2000)|IsPrime(p + 18) and IsPrime (p + 144)]; // Vincenzo Librandi, Oct 30 2012

Select[Prime[Range[2000]], And @@ PrimeQ[{# + 18, # + 144}]&] (* Vincenzo Librandi, Oct 30 2012 *)

13 inserted and extended by R. J. Mathar, Feb 19 2009

cp's OEIS Frontend

A031936 Lower prime of a difference of 18 between consecutive primes.

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A156104 Primes p such that p+36 is also prime.

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A153419 Primes p such that p+20 is also prime.

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A252089 Primes p such that p + 26 is prime.

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A156328 List of prime pairs of the form (p, p+18).

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A161723 Middle members p of prime triples (p-18,p,p+18).

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A231608 Table whose n-th row consists of primes p such that p + 2n is also prime, read by antidiagonals.

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Maple

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A156109 Primes p such that p+18 and p+36 are both prime.

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