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.

A096342 Primes of the form p*q + p + q, where p and q are two successive primes.

Original entry on oeis.org

11, 23, 47, 167, 251, 359, 479, 719, 1847, 2111, 2591, 3719, 6719, 7559, 8819, 10607, 12539, 14591, 19319, 27551, 29231, 31319, 51071, 53819, 68111, 97967, 149759, 155219, 172199, 177239, 195359, 199799, 234239, 273527, 305783, 314711, 339863
Offset: 1

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Author

Giovanni Teofilatto, Jun 29 2004

Keywords

Comments

a(n) == 3 mod 4.
Primes arising in A126148. - Jonathan Vos Post, Mar 08 2007
Number of primes <10^n: 0, 3, 8, 15, 26, 49, 99, 220, 514, 1228, 2991, 7746, 20218, 54081, ..., . - Robert G. Wilson v

Examples

			a(4)=167 because 11*13 + 11 + 13=167.

Links

Crossrefs

Cf. A000040, A001043, A006094, A126148, A126199.

Programs

  • Mathematica
    a = {}; Do[p = Prime[n]Prime[n + 1] + Prime[n] + Prime[n + 1]; If[ PrimeQ[p], AppendTo[a, p]], {n, 110}]; a (* Robert G. Wilson v, Jul 01 2004 *)
Select[Times@@#+Total[#]&/@Partition[Prime[Range[200]],2,1],PrimeQ] (* Harvey P. Dale, Nov 25 2018 *)
  • PARI
    list(lim)=my(v=List(),p=2,t); forprime(q=3,, t=p*q+p+q; if (t>lim, return(Set(v))); if(isprime(t), listput(v,t)); p=q) \\ Charles R Greathouse IV, Sep 15 2015

Extensions

More terms from Robert G. Wilson v, Jul 02 2004

A126148 Primes p such that pq+p+q is prime, where q is the next prime after p.

Original entry on oeis.org

2, 3, 5, 11, 13, 17, 19, 23, 41, 43, 47, 59, 79, 83, 89, 101, 109, 113, 137, 163, 167, 173, 223, 229, 257, 311, 383, 389, 409, 419, 439, 443, 479, 521, 547, 557, 577, 593, 613, 643, 647, 683, 773, 797, 809, 811, 853, 953, 983, 1019, 1049, 1097, 1109, 1151, 1171
Offset: 1

Views

Author

J. M. Bergot, Mar 07 2007

Keywords

Examples

			Take p = 13 and q = 17: product is 221 and sum is 30; add them to get 251, a prime. So 13 is a member.

Links

Crossrefs

Cf. A096342, A000040, A001043, A006094, A126199, A096342.

Programs

  • Maple
    a:=proc(n) if isprime(ithprime(n)*ithprime(n+1) +ithprime(n) +ithprime(n+1)) then ithprime(n) fi end: seq(a(n), n=1..250); # Emeric Deutsch, Mar 08 2007
  • Mathematica
    Prime@Select[Range[200], PrimeQ[Prime[ # ]Prime[ # + 1] + Prime[ # ] + Prime[ # + 1]] &] (* Ray Chandler, Mar 07 2007 *)
  • PARI
    v=List();p=2;forprime(q=3,1e4, if(isprime(p*q+p+q), listput(v,p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 26 2012

Extensions

Extended by Ray Chandler, Emeric Deutsch and Robert G. Wilson v, Mar 07 2007

A180617 Sum of divisors of the product of two consecutive primes.

Original entry on oeis.org

12, 24, 48, 96, 168, 252, 360, 480, 720, 960, 1216, 1596, 1848, 2112, 2592, 3240, 3720, 4216, 4896, 5328, 5920, 6720, 7560, 8820, 9996, 10608, 11232, 11880, 12540, 14592, 16896, 18216, 19320, 21000, 22800, 24016, 25912, 27552, 29232, 31320, 32760, 34944, 37248, 38412
Offset: 1

Views

Author

Thomas Kellar, Sep 12 2010

Keywords

Examples

			a(1) = sigma(2*3) = 12, a(2) = sigma(3*5) = 24.

Crossrefs

A distant relative of A054640.
Cf. A000203, A001043, A006094, A126199.

Programs

  • Magma
    [(1+NthPrime(n))*(1+NthPrime(n+1)): n in [1..50]]; // Vincenzo Librandi, Feb 16 2015
  • Mathematica
    DivisorSigma[1,#]&/@(Times@@@Partition[Prime[Range[50]],2,1]) (* Harvey P. Dale, Apr 04 2015 *)
Table[Prime[n]*Prime[n+1]+Prime[n]+Prime[n+1]+1,{n,1,30}] (* Metin Sariyar, Dec 08 2019 *)
  • PARI
    for (n=1,10, i=prod(x=n,n+1,prime(x)); p=sigma(i); print1(p, ", "); )
  • PARI
    a(n)=my(p=prime(n)); (p+1)*(nextprime(p+1)+1) \\ Charles R Greathouse IV, Feb 16 2015

Formula

a(n) = A000203(A006094(n)). - Omar E. Pol, Dec 08 2019
a(n) = A006094(n) + A001043(n) + 1. - Metin Sariyar, Dec 08 2019
a(n) = A126199(n) + 1 (after above formula). - Omar E. Pol, Dec 08 2019

Extensions

More terms from Vincenzo Librandi, Feb 16 2015
Name simplified by Omar E. Pol, Dec 08 2019

A284550 Integers n such that prime(n) + prime(n+1) + prime(n+2) + prime(n+3) + prime(n)*prime(n+1)*prime(n+2)*prime(n+3) is prime.

Original entry on oeis.org

1, 2, 9, 35, 45, 61, 80, 84, 97, 98, 124, 130, 140, 142, 175, 179, 185, 213, 241, 249, 287, 300, 324, 344, 346, 352, 366, 368, 369, 384, 389, 398, 400, 409, 431, 436, 437, 462, 515, 520, 525, 530, 544, 565, 592, 594, 595, 614, 615, 627, 628, 682, 719, 745, 778, 798, 835, 852, 861
Offset: 1

Views

Author

Zak Seidov, Mar 29 2017

Keywords

Examples

			n=1: 2+3+5+7+2*3*5*7=227=A000040(49),
n=2: 3+5+7+11+3*5*7*11=1181=A000040(194).

Links

Crossrefs

Cf. A000040, A096342, A126199.

Programs

Showing 1-4 of 4 results.

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