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.

A092729 Duplicate of A072667.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 29, 31, 41, 43, 61, 67, 73, 97, 113, 127, 151, 179, 191, 193, 199, 211, 223, 229, 239, 241, 271, 277, 281, 293, 307, 317, 337, 349, 367, 373, 379, 397, 401, 409, 419, 431, 439, 463, 487, 523, 541, 547, 577, 613, 619, 641, 643, 659, 683, 701, 709, 727
Offset: 1

Views

Author

Keywords

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

A177017 Primes prime(n) such that prime(n) + prime(n+1) + 1 is also prime.

Original entry on oeis.org

5, 7, 13, 17, 19, 23, 29, 37, 47, 53, 67, 79, 83, 97, 103, 109, 113, 131, 137, 163, 173, 181, 197, 227, 229, 251, 257, 269, 283, 293, 307, 313, 359, 383, 389, 401, 409, 421, 439, 449, 457, 467, 479, 491, 503, 509, 587, 593, 599, 613, 617, 643, 647, 659, 677
Offset: 1

Views

Author

Vincenzo Librandi, May 22 2010

Keywords

Links

Crossrefs

Cf. A072666, A072667.

Programs

  • Magma
    [NthPrime(n): n in [1..200] | IsPrime(NthPrime(n)+NthPrime(n+1)+1)]; // Vincenzo Librandi, Aug 26 2012
  • Mathematica
    Select[Prime[Range[200]],PrimeQ[#+NextPrime[#]+1]&] (* Vincenzo Librandi, Aug 26 2012 *)
Transpose[Select[Partition[Prime[Range[300]],2,1],PrimeQ[Total[#]+1]&]][[1]] (* Harvey P. Dale, Apr 16 2013 *)

Extensions

Edited and corrected by N. J. A. Sloane, Jun 22 2010

A072666 Numbers n such that prime(n) + prime(n+1) - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 21, 25, 30, 31, 36, 41, 43, 44, 46, 47, 48, 50, 52, 53, 58, 59, 60, 62, 63, 66, 68, 70, 73, 74, 75, 78, 79, 80, 81, 83, 85, 90, 93, 99, 100, 101, 106, 112, 114, 116, 117, 120, 124, 126, 127, 129, 130, 131, 132, 137, 138, 140, 145, 147, 149
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A000720, A072667, A072669, A177017.

Programs

  • Magma
    [n: n in [1..200] | IsPrime(NthPrime(n) + NthPrime(n+1)-1)] // Vincenzo Librandi, Aug 26 2012
  • Maple
    N:= 10^4: # to get all terms n such that prime(n+1) <= N
Primes:= select(isprime,[2,seq(2*i+1,i=1..floor(N/2))]):
PP:= Primes[1..-2]+Primes[2..-1]:
select(t -> isprime(PP[t]-1), [$1..nops(PP)]); # Robert Israel, Dec 11 2014
  • Mathematica
    Select[Range[200], PrimeQ[Prime[#]+Prime[#+1]-1] &] (* Harvey P. Dale, Dec 16 2010 *)

Formula

a(n) = pi(A072667(n)) = A000720(A072667(n)). - Zak Seidov, Dec 08 2014

Extensions

Definition clarified by Robert Israel, Dec 11 2014
Showing 1-4 of 4 results.

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

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