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 1-7 of 7 results.

A072669 Primes of the form prime(x) + prime(x+1) - 1.

Original entry on oeis.org

7, 11, 17, 23, 29, 41, 59, 67, 83, 89, 127, 137, 151, 197, 239, 257, 307, 359, 383, 389, 409, 433, 449, 461, 479, 491, 547, 557, 563, 599, 617, 647, 683, 701, 739, 751, 761, 797, 809, 827, 839, 863, 881, 929, 977, 1063, 1087, 1103, 1163, 1229, 1249, 1283, 1289, 1319, 1373
Offset: 1

Views

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Aug 12 2002

Keywords

Comments

Consider m such that prime(m) + prime(m+1) = prime(k) + 1 for some k; sequence gives prime(k).
A118072 is a subsequence, hence this sequence is infinite on Dickson's conjecture. - Charles R Greathouse IV, Apr 18 2013

Links

Crossrefs

Cf. A001043, A092738, A072666, A072667.

Programs

  • Mathematica
    f[n_] := Prime[n] + Prime[n + 1] - 1; f[ # ] & /@ Select[ Range[120], PrimeQ[ f[ # ]] &] (* Robert G. Wilson v, Apr 14 2004 *)
Select[Total[#]-1&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* Harvey P. Dale, Aug 06 2012 *)
  • PARI
    p=2;forprime(q=3,1e6,if(isprime(p+q-1),print1(p+q-1", "));p=q) \\ Charles R Greathouse IV, Apr 18 2013

Extensions

Definition reworded by Jorge Coveiro, Apr 12 2004
Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar

A207990 Primes of the form prime(n) + prime(n+1) - 5.

Original entry on oeis.org

3, 7, 13, 19, 31, 37, 47, 73, 79, 107, 139, 157, 167, 181, 193, 199, 211, 263, 271, 283, 347, 367, 379, 457, 467, 487, 503, 571, 613, 619, 643, 691, 757, 823, 859, 877, 887, 919, 941, 997, 1039, 1187, 1231, 1279, 1307, 1423, 1489, 1579, 1601, 1627, 1663
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2012

Keywords

Links

Crossrefs

Cf. A072669, A092738.

Programs

  • Mathematica
    Select[Table[Prime[n] + Prime[n + 1] - 5, {n, 200}], PrimeQ]
Select[Total/@Partition[Prime[Range[200]],2,1]-5,PrimeQ] (* Harvey P. Dale, Apr 05 2020 *)
  • PARI
    p=2;forprime(q=3,1e4,if(isprime(t=p+q-5),print1(t", "));p=q) \\ Charles R Greathouse IV, Apr 13 2012

A093734 Primes p such that both prime(p) + prime(p+1) +/-1 are also primes.

Original entry on oeis.org

3, 19, 79, 127, 131, 149, 373, 401, 487, 1031, 1303, 1427, 1699, 1801, 2069, 2477, 2659, 2767, 3307, 3391, 3449, 3583, 3671, 3727, 4093, 4423, 4603, 4817, 5081, 5501, 5641, 5737, 5813, 5839, 6619, 7219, 7243, 7351, 7393, 8293, 8543, 8641, 8693, 8699
Offset: 1

Views

Author

Robert G. Wilson v and Jorge Coveiro, Apr 14 2004

Keywords

Links

Crossrefs

Cf. A072669, A092738.

Programs

  • Mathematica
    Select[ Range[ 10000 ], PrimeQ[ # ] && PrimeQ[ Prime[ # ] + Prime[ # + 1 ] - 1 ] && PrimeQ[ Prime[ # ] + Prime[ # + 1 ] + 1 ] & ]

A157995 Primes which are the sum of 1 plus two consecutive not-twin primes, p1 and p2, (p2-p1)>2.

Original entry on oeis.org

19, 31, 43, 53, 79, 101, 113, 139, 163, 173, 199, 211, 223, 241, 269, 331, 353, 373, 463, 509, 521, 577, 601, 619, 631, 727, 773, 787, 811, 829, 853, 883, 907, 919, 947, 967, 991, 1013, 1031, 1181, 1193, 1231, 1291, 1301, 1361, 1429, 1447, 1483, 1531, 1543
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 11 2009

Keywords

Examples

			19=7+11+1, 31=13+17+1, 43=19+23+1, 53=23+29+1, 79=37+41+1, 101=47+53+1, ...

Links

Crossrefs

Cf. A005385, A092738, A118071.

Programs

  • Maple
    count:= 0: R:= NULL: p:= 2:
while count < 100 do
  q:= p; p:= nextprime(p);
  if p-q > 2 and isprime(p+q+1) then
     count:= count+1; R:= R, p+q+1
  fi
od:
R; # Robert Israel, May 13 2020
  • Mathematica
    lst={};Do[p0=Prime[n];p1=Prime[n+1];a=p0+p1+1;If[PrimeQ[a]&&(p1-p0)>2,AppendTo[lst,a]],{n,6!}];lst
Select[Total[#]+1&/@Select[Partition[Prime[Range[200]],2,1],Last[#]-First[#]>2&],PrimeQ]  (* Harvey P. Dale, Mar 13 2011 *)

Extensions

Definition corrected by Harvey P. Dale, Mar 13 2011

A157996 Primes which are sum of 1 and two nonconsecutive primes p1 and p2, p2 - p1 > 2.

Original entry on oeis.org

11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 11 2009

Keywords

Comments

Conjecture: for n > 1, a(n) = prime(n+5). - Charles R Greathouse IV, Mar 12 2012
A185154(n) is the smallest prime q, such that A049084(q) + 1 < A049084(a(n) - q - 1). - Reinhard Zumkeller, Mar 12 2012

Examples

			11=3+7+1, 17=5+11+1, 19=5+13+1, ...

Links

Crossrefs

Cf. A000040, A076805, A005385, A092738, A118071, A157995, A065091, A006093.

Programs

  • Haskell
    a157996 n = a157996_list !! (n-1)
a157996_list = map (+ 1) $ filter f a006093_list where
   f x = g $ takeWhile (< x) a065091_list where
     g []  = False
     g [_] = False
     g (p:ps@(_:qs)) = (x - p) `elem` qs || g ps
-- Reinhard Zumkeller, Mar 12 2012
  • Mathematica
    lst={};Do[p0=Prime[n];Do[px=Prime[n+k];If[PrimeQ[a=p0+px+1],AppendTo[lst,a]],{k,2,2*5!}],{n,6!}];Take[Union[lst],222]
  • PARI
    is(n)=if(!isprime(n),return(0)); my(p=3,q=5); forprime(r=7,n-4, if(isprime(n-1-r) && n-1-r <= p, return(1)); p=q; q=r); 0 \\ Charles R Greathouse IV, Nov 05 2015

A207991 Primes of the form prime(n) + prime(n+1) + 5.

Original entry on oeis.org

13, 17, 23, 29, 41, 47, 73, 83, 89, 149, 157, 167, 191, 227, 263, 281, 293, 313, 389, 401, 439, 461, 467, 563, 569, 653, 673, 701, 757, 857, 877, 887, 911, 929, 971, 983, 1049, 1069, 1093, 1109, 1153, 1213, 1277, 1289, 1433, 1451, 1487, 1499, 1523, 1637
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2012

Keywords

Links

Crossrefs

Cf. A072669, A092738, A207990.

Programs

  • Mathematica
    Select[Table[Prime[n] + Prime[n + 1] + 5, {n, 200}], PrimeQ]
Select[Total[#]+5&/@Partition[Prime[Range[300]],2,1],PrimeQ] (* Harvey P. Dale, Dec 28 2021 *)
  • PARI
    p=2;forprime(q=3,1e4,if(isprime(t=p+q+5),print1(t", "));p=q) \\ Charles R Greathouse IV, Apr 13 2012

A207992 Primes p of the form p = prime(n) + prime(n+1) - 5 and p = prime(k) + prime(k+1) + 5.

Original entry on oeis.org

13, 47, 73, 157, 167, 263, 467, 757, 877, 887, 2027, 2593, 3203, 3733, 4273, 4703, 4787, 5087, 5387, 6373, 6637, 7393, 7823, 8893, 9587, 10007, 10163, 12433, 13933, 15083, 15287, 15373, 16333, 17387, 17483, 18013, 18313, 19237, 19477, 20327, 21467, 23567
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Feb 22 2012

Keywords

Comments

n = k+1 or k+2. - Charles R Greathouse IV, Apr 16 2012

Examples

			3+5+5 = 13 = 7+11-5, 23+29-5 = 47 = 19+23+5

Links

Crossrefs

Cf. A072669, A092738, A207990, A207991.

Programs

  • Mathematica
    a1 = Select[Table[Prime[n] + Prime[n + 1] - 5, {n, 2010}], PrimeQ]; a2 = Select[Table[Prime[n] + Prime[n + 1] + 5, {n, 2000}], PrimeQ]; Intersection[a1, a2]
With[{pr=Transpose[#+{5,-5}&/@Total/@Partition[Prime[Range[3000]],2,1]]}, Select[Intersection[pr[[1]],pr[[2]]], PrimeQ]] (* Harvey P. Dale, Mar 13 2013 *)
  • PARI
    p=2;q=3;r=5;forprime(s=7,1e4,if((r==p+10||r+s==p+q+10) && isprime(p+q+5), print1(p+q+5", "));p=q;q=r;r=s) \\ Charles R Greathouse IV, Apr 16 2012
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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