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 11-16 of 16 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 *)

A339414 Primes p such that (p+q)/4 is prime, where q is the next prime after p.

Original entry on oeis.org

3, 5, 23, 31, 83, 131, 251, 271, 331, 383, 443, 563, 971, 1123, 1223, 1231, 1283, 1291, 1543, 2063, 2371, 2383, 2551, 2851, 2903, 2963, 3083, 3323, 3691, 3889, 4051, 4283, 4591, 4733, 4831, 4871, 4951, 5003, 5209, 5351, 5683, 5711, 5851, 6229, 6271, 6323, 6491, 6863, 6911, 7393, 7451, 7583, 7643
Offset: 1

Views

Author

Robert Israel, Dec 03 2020

Keywords

Comments

After the initial 2 terms, a(n)=2*A118134(n)-3. - Hugo Pfoertner, Dec 03 2020

Examples

			a(5)=83 is in the sequence because it is prime, the next prime is 89, and (83+89)/4 = 43 is prime.

Links

Crossrefs

Subset of A098058.
Cf. A118134.

Programs

  • Maple
    P:= select(isprime, [seq(i,i=3..10000,2)]):
R:= (P[1..-2]+P[2..-1])/4:
P[select(i-> R[i]::integer and isprime(R[i]), [$1..nops(R)])];
  • PARI
    isok(p) = isprime(p) && iferr(isprime((p+nextprime(p+1))/4),E,0); \\ Michel Marcus, Dec 04 2020

A154942 Primes p such that (p-1)*p*(p+1)-p-2 and (p-1)*p*(p+1)+p+2 are primes.

Original entry on oeis.org

3, 5, 29, 71, 113, 263, 1103, 2339, 3203, 3413, 3593, 3659, 3719, 4421, 5939, 6269, 7841, 9011, 9029, 13121, 13841, 14423, 15671, 17033, 19073, 22079, 22811, 26783, 27851, 28949, 29303, 30839, 31973, 32063, 32141, 34301, 38543, 38873, 39119
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Comments

2*3*4=24-3-2=19, 2*3*4=24+3+2=29, ...

Crossrefs

Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*p*(p+1)-p-2]&&PrimeQ[(p-1)*p*(p+1)+p+2],AppendTo[lst,p]],{n,8!}];lst
prQ[n_]:=Module[{x=n^3-n,y=n+2},And@@PrimeQ[{x+y,x-y}]]; Select[Prime[ Range[4200]],prQ] (* Harvey P. Dale, Jun 21 2012 *)

A154941 Sophie Germain primes in A154939.

Original entry on oeis.org

3, 5, 11, 131, 419, 1409, 2069, 3449, 3761, 3911, 6899, 7079, 7151, 9539, 9791, 10529, 10691, 11321, 11831, 14741, 15269, 17291, 22079, 27281, 27809, 30449, 34439, 45131, 48479, 52289, 54251, 64439, 70901, 75389, 78839, 85691, 101411, 102911
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Comments

2*3+1=7, 5*2+1=11, ...

Crossrefs

Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*(p+1)-p]&&PrimeQ[(p-1)*(p+1)+p],If[PrimeQ[p*2+1],AppendTo[lst,p]]],{n,8!}];lst
Select[Prime[Range[10000]],AllTrue[{2#+1,(#-1)(#+1)+#,(#-1)(#+1)-#},PrimeQ]&] (* Harvey P. Dale, Sep 21 2023 *)

A154944 Primes p such that (p-1)*p*(p+1)-p+2 and (p-1)*p*(p+1)+p-2 are primes.

Original entry on oeis.org

19, 37, 67, 151, 367, 859, 1471, 2791, 2971, 3061, 4357, 4447, 4507, 6367, 7159, 7237, 7591, 8311, 8647, 11617, 12211, 12601, 13249, 14947, 15271, 15661, 16699, 18097, 19777, 20149, 20347, 20947, 21019, 22741, 23311, 23857, 24019, 25867, 26701
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Keywords

Crossrefs

Cf. A053184, A038872, A141158, A038615, A098058, A038936, A089270, A140559, A154939, A154942

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[(p-1)*p*(p+1)-p+2]&&PrimeQ[(p-1)*p*(p+1)+p-2],AppendTo[lst,p]],{n,8!}];lst

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 11-16 of 16 results.

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