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.

Previous Showing 11-17 of 17 results.

A155009 Primes p such that (p-a)*(p+a)-+a*p are primes,a=5.

Original entry on oeis.org

2, 7, 11, 17, 19, 23, 41, 43, 61, 67, 107, 109, 131, 137, 179, 197, 263, 269, 331, 353, 397, 641, 677, 743, 859, 941, 1163, 1171, 1213, 1303, 1319, 1433, 1447, 1453, 1543, 1601, 1783, 2221, 2351, 2371, 2417, 2503, 2657, 2689, 2791, 2797, 2909, 3037, 3301
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

Keywords

Comments

1*12-35=-23, 1*12+35=47; 6*16-55=96-55=41, 6*16-55=96+55=151, ...

Links

Crossrefs

Cf. A125272, A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A155006, A155007, A155008

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[(p-5)*(p+5)-5*p]&&PrimeQ[(p-5)*(p+5)+5*p],AppendTo[lst,p]],{n,7!}];lst
Select[Prime[Range[500]],AllTrue[(#-5)(#+5)+{5#,-5#},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 01 2016 *)

A164567 Primes p such that 5*p-6 and 5*p+6 are prime numbers.

Original entry on oeis.org

5, 7, 13, 19, 29, 37, 41, 47, 79, 83, 97, 103, 149, 163, 211, 257, 293, 313, 359, 379, 401, 421, 449, 509, 523, 541, 547, 601, 643, 653, 673, 691, 701, 733, 821, 853, 883, 911, 929, 937, 1009, 1129, 1171, 1217, 1367, 1381, 1423, 1511, 1567, 1619, 1637, 1787
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Primes of the form A087681(k)/5, any k [R. J. Mathar, Sep 17 2009]

Crossrefs

Cf. A106015, A124098, A125272, A127430, A164566

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[5*p-6]&&PrimeQ[5*p+6],AppendTo[lst,p]], {n,6!}];lst
Select[Prime[Range[300]],AllTrue[5#+{6,-6},PrimeQ]&] (* Harvey P. Dale, Jun 09 2022 *)

A164570 Primes p such that 8*p-3 and 8*p+3 are also prime numbers.

Original entry on oeis.org

2, 5, 7, 13, 47, 103, 107, 127, 163, 233, 293, 337, 383, 433, 443, 467, 503, 673, 677, 733, 797, 877, 1087, 1093, 1153, 1217, 1223, 1307, 1637, 1933, 2053, 2087, 2137, 2423, 2477, 2543, 2633, 2687, 2857, 2917, 3163, 3373, 3407, 3467, 3767, 3793, 3877
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Subsequence of A023229. [R. J. Mathar, Aug 26 2009]
Primes of the form A087695(k)/8. [R. J. Mathar, Aug 26 2009]

Examples

			For p=2, 8*2-3=13 and 8*2+3=19 are prime numbers, which adds p=2 to the sequence
For p=5, 8*5-3=37 and 8*5+3=43 are prime numbers, which adds p=5 to the sequence.

Links

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239, A060212, A106015, A124098, A125272, A127430, A153768, A164566, A164567, A164568, A164569.

Programs

  • Magma
    [p: p in PrimesUpTo(3000) | IsPrime(8*p-3) and IsPrime(8*p+3)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[8*p-3]&&PrimeQ[8*p+3],AppendTo[lst,p]], {n,7!}];lst
Select[Prime[Range[1000]], And@@PrimeQ/@{8 # + 3, 8 # - 3}&] (* Vincenzo Librandi, Apr 09 2013 *)
Select[Prime[Range[1000]],AllTrue[8#+{3,-3},PrimeQ]&] (* Harvey P. Dale, May 05 2023 *)

Extensions

Comments turned into examples by R. J. Mathar, Aug 26 2009

A171518 Primes p such that 3*p-+8 are primes.

Original entry on oeis.org

5, 7, 13, 17, 53, 73, 83, 113, 127, 157, 193, 223, 277, 347, 367, 433, 613, 647, 673, 743, 797, 907, 937, 1117, 1217, 1373, 1427, 1483, 1543, 1597, 1637, 1667, 1877, 1933, 2027, 2237, 2297, 2447, 2647, 2687, 2843, 3083, 3137, 3613, 3797, 4073, 4463, 4483
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2009

Keywords

Examples

			5 is in the sequence since 3*5-8=7 and 3*5+8=23 are primes.

Links

Crossrefs

Cf. A000040, A005382, A005384, A023204-A023207, A063908-A063912, A103803, A124098, A125272, A171517

Programs

  • Mathematica
    Select[Prime[Range[7! ]],PrimeQ[3*#-8]&&PrimeQ[3*#+8]&]
Select[Prime[Range[700]],AllTrue[3#+{8,-8},PrimeQ]&] (* Harvey P. Dale, Feb 10 2025 *)

A120637 Primes such that their triple is 2 away from a prime number.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 97, 103, 113, 127, 137, 139, 149, 163, 167, 173, 181, 191, 193, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 271, 277, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367, 373, 383
Offset: 1

Views

Author

Cino Hilliard, Aug 17 2006

Keywords

Comments

This sequence is a variation of the sequence in the reference. However, this sequence should have an infinite number of terms.

Examples

			19 is a prime and 19*3 = 57 which is two away from 59 which is prime.
31 is not in the table because 31*3 = 93 which is 2 away from 91 and 95, both not prime.

References

  • R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.18.

Crossrefs

Cf. A125272.

Programs

  • Mathematica
    Select[Prime[Range[200]],PrimeQ[3#+2]||PrimeQ[3#-2]&] (* Harvey P. Dale, Aug 10 2011 *)
  • PARI
    primepm2(n,k) { local(x,p1,p2,f1,f2,r); if(k%2,r=2,r=1); for(x=1,n, p1=prime(x); p2=prime(x+1); if(isprime(p1*k+r)||isprime(p1*k-r), print1(p1",") ) ) }

Formula

Union of A023208 and A088878.

A120638 Primes such that their triple is not 2 away from a prime number.

Original entry on oeis.org

2, 31, 41, 73, 101, 107, 109, 131, 151, 157, 179, 223, 229, 241, 281, 283, 311, 359, 379, 389, 421, 449, 463, 509, 521, 547, 563, 571, 599, 613, 617, 619, 631, 641, 647, 653, 661, 683, 691, 701, 719, 733, 739, 743, 773, 787, 809, 811, 821, 827, 829, 839, 857
Offset: 1

Views

Author

Cino Hilliard, Aug 17 2006

Keywords

Comments

This sequence is a variation of the sequence in the reference. However, this sequence should have an infinite number of terms. k=2 in the PARI code.

Examples

			31*3 = 93 which is two away from 91 and 95 both not prime.

References

  • R. Crandall and C. Pomerance, Prime Numbers A Computational Perspective, Springer Verlag 2002, p. 49, exercise 1.18.

Crossrefs

Cf. A023208, A088878, A125272.

Programs

  • Mathematica
    Select[Prime@Range@200,!PrimeQ[3#-2]&&!PrimeQ[3#+2]&] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2011 *)
Select[Prime[Range[200]],NoneTrue[3#+{2,-2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 01 2019 *)
  • PARI
    primepm3(n,k) = =number of iterations,k = factor { local(x,p1,p2,f1,f2,r); if(k%2,r=2,r=1); for(x=1,n, p1=prime(x); p2=prime(x+1); if(!isprime(p1*k+r)&!isprime(p1*k-r), print1(p1",") ) ) }

A155010 Primes p such that (p-a)*(p+a)-+a*p and (p-b)*(p+b)-+b*p are primes, a=2,b=3.

Original entry on oeis.org

7, 37, 587, 28703, 35677, 36857, 99367, 326707, 361687, 578167, 613573, 619007, 656407, 688783, 702203, 713467, 874823, 922027, 940573, 1045763, 1057907, 1244687, 1371157, 1419697, 1555187, 1665767, 1687187, 1687327, 1799453
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

Keywords

Crossrefs

Cf. A125272, A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A155006, A155007, A155008, A155009

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[(p-2)*(p+2)-2*p]&&PrimeQ[(p-2)*(p+2)+2*p]&&PrimeQ[(p-3)*(p+3)-3*p]&&PrimeQ[(p-3)*(p+3)+3*p],AppendTo[lst,p]],{n,9!}];lst
Select[Prime[Range[200000]],AllTrue[Flatten[{(#-2)(#+2)+{2#,-2#},(#-3)(#+3)+ {3#,-3#}}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 26 2015 *)
Previous Showing 11-17 of 17 results.

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