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 11-14 of 14 results.

A106077 Primes p such that 5*p + 2 and 2*p + 5 are primes.

Original entry on oeis.org

3, 7, 13, 19, 31, 61, 67, 73, 79, 97, 109, 151, 181, 313, 373, 457, 523, 541, 613, 643, 661, 709, 727, 739, 769, 811, 859, 991, 997, 1039, 1069, 1087, 1171, 1249, 1321, 1327, 1381, 1399, 1483, 1657, 1663, 1693, 1747, 1777, 1801, 1867, 2053, 2113, 2239, 2251
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Cf. A023217.

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | IsPrime(5*p+2) and IsPrime(2*p+5)]; // Vincenzo Librandi, Nov 13 2010
  • Maple
    filter:= proc(p) isprime(p) and isprime(5*p+2) and isprime(2*p+5) end proc:
select(filter, [seq(i,i=3..3000,2)]); # Robert Israel, Aug 25 2025
  • Mathematica
    Select[Prime[Range[220]], PrimeQ[2#+5]&&PrimeQ[5#+2]&]

Extensions

More terms from Vincenzo Librandi, Mar 28 2010

A164569 Primes p such that 11*p+8 are prime numbers.

Original entry on oeis.org

3, 13, 31, 73, 79, 151, 163, 181, 193, 241, 283, 349, 373, 379, 409, 421, 463, 601, 631, 673, 751, 769, 811, 829, 853, 883, 991, 1021, 1039, 1063, 1171, 1201, 1303, 1381, 1423, 1429, 1453, 1459, 1471, 1543, 1549, 1579, 1609, 1621, 1663, 1669, 1789, 1801
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2009

Keywords

Comments

Apart from the first term, a(n) = 1 (mod 6).

Examples

			11*3+8=41, ..

Crossrefs

Cf. A023212, A023217, A023224, A023230, A023239

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[11*p+8],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[500]],PrimeQ[11#+8]&] (* Harvey P. Dale, Jul 17 2011 *)

Extensions

Comment from Charles R Greathouse IV, Oct 12 2009

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

A342814 Numbers k such that k - 1 and floor(k/5) are both prime.

Original entry on oeis.org

12, 14, 18, 38, 68, 98, 158, 308, 338, 368, 398, 488, 548, 758, 788, 908, 968, 998, 1118, 1568, 1658, 1748, 1868, 1988, 2288, 2438, 2618, 2708, 2858, 2888, 3038, 3068, 3218, 3308, 3458, 3548, 3638, 3698, 3848, 4058
Offset: 1

Views

Author

Claude H. R. Dequatre, Mar 22 2021

Keywords

Comments

Except for a(1) and a(2), all terms == 8 (mod 10).
The first three absolute differences (d) between two consecutive floor(k/5) are respectively equal to 0, 1 and 4 and all the others to 6 or a multiple of 6.
Subsequence of A008864, by definition. - Michel Marcus, Mar 22 2021
For n >= 3, a(n) = 5*A023217(n-2) + 3. Higher terms also coincide with A265767 + 1. - Hugo Pfoertner, Mar 22 2021

Examples

			12 is a term because 12 - 1 = 11 and 11 is prime and 12/5 = 2.4 whose floor value is 2 and 2 is also prime.
97 is not a term because 97 - 1 = 96 and 96 is not prime although floor(97/5) = 19 is prime.
Initial terms, associated primes and d:
          k       k - 1     floor(k/5)     d
a(1)     12        11          2
a(2)     14        13          2           0
a(3)     18        17          3           1
a(4)     38        37          7           4
a(5)     68        67         13           6
a(6)     98        97         19           6
a(7)    158       157         31          12
a(8)    308       307         61          30
a(9)    338       337         67           6
a(10)   368       367         73           6

Links

Crossrefs

Cf. A000040, A007530, A007811, A014561, A259645.
Cf. A008864, A023217, A265767.

Programs

  • Maple
    R:= NULL:
p:= 1: count:= 0:
while count < 100 do
  p:= nextprime(p);
  if isprime(floor((p+1)/5)) then
     R:= R,p+1; count:= count+1
  fi
od:
R; # Robert Israel, May 22 2024
  • Mathematica
    Select[Range[2,5000,2],And@@PrimeQ[{#-1,Floor[#/5]}]&] (* Giorgos Kalogeropoulos, Apr 01 2021 *)
  • PARI
    for(k = 1,10000,if(isprime(k - 1) && isprime(k\5),print1(k", ")))
Previous Showing 11-14 of 14 results.

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