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 1-4 of 4 results.

A137796 Prime numbers p such that p + 12 and p - 12 are primes.

Original entry on oeis.org

17, 19, 29, 31, 41, 59, 71, 101, 139, 151, 179, 211, 239, 251, 269, 281, 409, 421, 431, 479, 491, 619, 631, 739, 809, 941, 1009, 1021, 1051, 1289, 1291, 1439, 1459, 1471, 1499, 1511, 1571, 1609, 1709, 1721, 1789, 1889, 1901, 1999, 2099, 2141, 2281, 2411
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 28 2008

Keywords

Examples

			17 + 12 = 29 (a prime), 17 - 12 = 5 (a prime);
19 + 12 = 31 (a prime), 19 - 12 = 7 (a prime).

Links

Crossrefs

Cf. A092216, A046133. Note that this is different from A137873.

Programs

  • Maple
    isA092216 := proc(n) RETURN(isprime(n) and isprime(n-12) ) ; end: isA046133 := proc(n) RETURN(isprime(n) and isprime(n+12) ) ; end: isA137796 := proc(n) RETURN(isA092216(n) and isA046133(n)) ; end: for i from 1 to 400 do if isA137796(ithprime(i)) then printf("%d,",ithprime(i)) ; fi ; od: # R. J. Mathar, May 03 2008
  • Mathematica
    a=12; Select[Table[Prime[n],{n,10^3}], PrimeQ[ #-a] && PrimeQ[ #+a] &]
  • PARI
    lista(nn) = forprime(p=2, nn, if (isprime(p-12) && isprime(p+12), print1(p, ", "))); \\ Michel Marcus, Oct 04 2015

Formula

A092216 INTERSECT A046133. - R. J. Mathar, May 03 2008

Extensions

Corrected and extended by R. J. Mathar, May 03 2008

A163111 Prime numbers with gaps larger than 18 towards both neighboring primes.

Original entry on oeis.org

3967, 11027, 11657, 14107, 16033, 16787, 18013, 18617, 18637, 18839, 19661, 21247, 23719, 24281, 24571, 29101, 30367, 31357, 32749, 33247, 33679, 33997, 35201, 36037, 37747, 38501, 40063, 40387, 42533, 42611, 43691, 43913, 44417, 46957
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 20 2009

Keywords

Links

Crossrefs

Cf. A137875, A137874, A137873, A137872, A137871

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[ !PrimeQ[p-2]&&!PrimeQ[p+2]&&!PrimeQ[p-4]&&!PrimeQ[p+4]&&!PrimeQ[p-6]&&!PrimeQ[p+6]&& !PrimeQ[p-8]&&!PrimeQ[p+8]&&!PrimeQ[p-10]&&!PrimeQ[p+10]&&!PrimeQ[p-12]&&!PrimeQ[p+12]&&!PrimeQ[p-14]&&!PrimeQ[p+14]&&!PrimeQ[p-16]&&!PrimeQ[p+16]&&!PrimeQ[p-18]&&!PrimeQ[p+18], AppendTo[lst,p]],{n,8!}];lst
Select[Partition[Prime[Range[5000]],3,1],Min[Differences[#]]>18&][[All,2]] (* Harvey P. Dale, Jul 08 2021 *)

Formula

{A000040(i) : A001223(i) > 18 and A001223(i-1) > 18}. - R. J. Mathar, Jul 27 2009

Extensions

Definition rephrased by R. J. Mathar, Jul 27 2009

A163112 Prime numbers with gaps larger than 20 towards both neighboring primes.

Original entry on oeis.org

16033, 16787, 18013, 23719, 24281, 29101, 32749, 33247, 33679, 33997, 37747, 38501, 40063, 40387, 42533, 42611, 44417, 46957, 51109, 51383, 53479, 54217, 55291, 55763, 56333, 56569, 58271, 58511, 58831, 59833, 61441, 61781, 62273, 66137, 66271, 69593, 69623
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 20 2009

Keywords

Comments

Subsequence of A163111.

Links

Crossrefs

Cf. A137875, A137874, A137873, A137872, A137871, A163111.

Programs

  • Maple
    p := 2; q := 3; r := 3; for n from 2 to 15000 do if q-p > 20 and r-q > 20 then printf("%d,",q) ; fi; p := q; q := r; r := nextprime(r) ; od: # R. J. Mathar, Jul 27 2009
  • Mathematica
    Select[Partition[Prime[Range[7000]],3,1],Min[Differences[#]]>20&] [[All, 2]] (* Harvey P. Dale, Mar 16 2017 *)

Formula

{A000040(i) : A001223(i) > 20 and A001223(i-1) > 20}. - R. J. Mathar, Jul 27 2009

Extensions

Definition rephrased by R. J. Mathar, Jul 27 2009

A167840 Six-times-isolated primes: primes p such that none of p+-2, p+-4, p+-6, p+-8, p+-10 nor p+-12 are prime.

Original entry on oeis.org

2, 1847, 2179, 2503, 2819, 3137, 3433, 3967, 4177, 4621, 4831, 5623, 5953, 6637, 7283, 7369, 7393, 7433, 7621, 7993, 8039, 8147, 9257, 9587, 10753, 11027, 11197, 11213, 11369, 11657, 13063, 13367, 13381, 13537, 13553, 13649, 13859, 14107, 14221, 14369, 14503
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2009, Mar 26 2010

Keywords

Comments

Essentially the same as A137873. - R. J. Mathar, Dec 06 2009

Examples

			a(1)=2 (-10,-8,-6,-4,-2,0,4,6,8,10,12 are nonprimes);
a(2)=1847 (1835,1837,1839,1841,1843,1845,1849,1851,1853,1855,1857,1859 are nonprimes).

Links

Crossrefs

Cf. A000040, A137873, A167771, A167839.

Programs

  • Maple
    q:= p-> not ormap(isprime, [seq([p+i, p-i][], i=2..12, 2)]):
select(q, [ithprime(i)$i=1..2000])[];  # Alois P. Heinz, Jan 03 2022

Extensions

More terms from Dmitry Kamenetsky, Nov 30 2009
Missing term 13553 inserted by Alois P. Heinz, Jan 03 2022
Showing 1-4 of 4 results.

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