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 1-10 of 11 results. Next

A231383 Primes p such that p + 3*k is also prime, where p is k-th prime.

Original entry on oeis.org

2, 7, 13, 19, 29, 37, 53, 71, 101, 107, 131, 139, 163, 173, 181, 199, 223, 229, 263, 281, 293, 311, 337, 397, 443, 463, 491, 557, 569, 659, 673, 719, 733, 787, 809, 827, 839, 857, 953, 983, 1013, 1069, 1091, 1109, 1151, 1223, 1249, 1283, 1307, 1451, 1493, 1549
Offset: 1

Views

Author

K. D. Bajpai, Nov 08 2013

Keywords

Examples

			a(5)= 29 which is 10th prime.  prime(10)+3*10= 29+30= 59 which is also prime.
a(7)= 53 which is 16th prime.  prime(16)+3*16= 53+48= 101 which is also prime.

Links

Crossrefs

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A231232 (primes p : p+2*k is also prime).

Programs

  • Magma
    [NthPrime(n): n in [1..250] | IsPrime(NthPrime(n)+3*n)]; // Vincenzo Librandi, Jan 19 2015
  • Maple
    KD := proc() local a, b;  a:= ithprime(n); b:= a+3*n; if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..500);
  • Mathematica
    KD = Select[Table[{Prime[n], Prime[n] + 3*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[KD][[1]]
  • PARI
    is(n)=isprime(n) && isprime(n+3*primepi(n)) \\ Charles R Greathouse IV, Nov 08 2013

A254462 Primes prime(n) such that prime(n) + 5*n is also prime.

Original entry on oeis.org

2, 3, 13, 19, 29, 37, 43, 61, 113, 151, 163, 173, 223, 229, 239, 251, 311, 317, 337, 359, 373, 397, 409, 433, 503, 601, 647, 659, 673, 683, 757, 821, 857, 863, 887, 941, 1061, 1097, 1109, 1123, 1213, 1249, 1291, 1307, 1373, 1423, 1439, 1493, 1511, 1531, 1559
Offset: 1

Views

Author

Vincenzo Librandi, Feb 04 2015

Keywords

Examples

			prime(2)=3 is in the sequence because 3+5*2 = 13 is prime.
prime(6)=13 is in the sequence because 13+5*6 = 43 is prime.

Links

Crossrefs

Cf. A061067, A076300, A231232, A231383.

Programs

  • Magma
    [NthPrime(n): n in [1..300] | IsPrime(NthPrime(n)+5*n)];
  • Maple
    P:= select(isprime, [2,seq(i,i=3..10000,2)]):
P[select(i -> isprime(P[i]+5*i),[$1..nops(P)])]; # Robert Israel, Aug 01 2024
  • Mathematica
    Prime[Select[Range[300], PrimeQ[Prime[#] + 5 #] &]]

A231326 Primes p such that p - 2*k is also prime, where p is k-th prime.

Original entry on oeis.org

17, 19, 23, 37, 47, 67, 71, 73, 83, 89, 97, 113, 131, 137, 139, 149, 151, 157, 167, 179, 181, 197, 199, 223, 233, 263, 307, 331, 353, 379, 397, 419, 421, 439, 443, 457, 461, 463, 503, 557, 587, 613, 631, 641, 643, 659, 661, 677, 701, 719, 743, 761, 773, 839, 863
Offset: 1

Views

Author

K. D. Bajpai, Nov 07 2013

Keywords

Examples

			a(2)= 19 which is 8th prime. prime(8)-2*8= 19-16= 3 which is also prime.
a(6)= 67 which is 19th prime. prime(19)-2*19= 67-38= 29 which is also prime.

Links

Crossrefs

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A227420 (primes: p - pi(p) is also prime).
Cf. A231232 (primes: prime(k)+2*k is also prime).

Programs

  • Maple
    KD := proc() local a,b; a:= ithprime(n); b := a-2*n; if isprime(b) then RETURN (a); fi;end: seq(KD(),n=1..500);
  • Mathematica
    TK = Select[Table[{Prime[n], Prime[n] - 2*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[TK][[1]]

A231506 Primes p such that p + 3*k and p - 3*k, both are primes, where p is k-th prime.

Original entry on oeis.org

7, 13, 19, 53, 71, 101, 107, 139, 173, 199, 223, 229, 281, 293, 397, 463, 557, 569, 673, 787, 809, 839, 953, 1013, 1283, 1451, 1559, 1657, 1861, 1871, 1877, 1949, 1987, 1997, 2213, 2311, 2347, 2357, 2377, 2503, 2543, 2551, 2593, 2633, 2837, 2851, 2939, 2999, 3041
Offset: 1

Views

Author

K. D. Bajpai, Nov 09 2013

Keywords

Examples

			a(7)= 107 which is 28th prime. prime(28)-3*28= 107-84= 23: prime(28)+3*28= 107+84= 191: 23 and 191 both are primes.
a(9)= 173 which is 40th prime. prime(40)-3*40= 173-120= 53: prime(40)+3*40= 173+120= 293: 53 and 293 both are primes.

Links

Crossrefs

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A231232 (primes p : p+2*k is also primes).
Cf. A231383 (primes p : p+3*k is also primes).

Programs

  • Maple
    KD := proc() local a,b,d;  a:= ithprime(n); b:= abs(a-3*n);d:=(a+3*n); if isprime(b) and  isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..500);

A254665 Primes prime(n) such that prime(n) + 7*n is also prime.

Original entry on oeis.org

3, 71, 79, 89, 101, 199, 271, 281, 293, 349, 359, 433, 463, 479, 569, 577, 641, 659, 701, 743, 769, 787, 809, 839, 863, 911, 953, 1013, 1033, 1049, 1109, 1181, 1249, 1277, 1321, 1361, 1399, 1429, 1451, 1459, 1481, 1511, 1549, 1571, 1627, 1693, 1733, 1759, 1889
Offset: 1

Views

Author

Vincenzo Librandi, Feb 04 2015

Keywords

Examples

			prime(2)=3 is in the sequence because 3+7*2 = 17 is prime.
prime(20)=71 is in the sequence because 71+7*20 = 211 is prime.

Crossrefs

Cf. A061067, A231232, A231383, A254462.

Programs

  • Magma
    [NthPrime(n): n in [1..300] | IsPrime(NthPrime(n)+7*n)];
  • Mathematica
    Prime[Select[Range[300], PrimeQ[Prime[#] + 7# ]&]]

A254672 Primes prime(n) such that prime(n) + 6*n is also prime.

Original entry on oeis.org

5, 7, 11, 17, 19, 29, 31, 37, 43, 47, 53, 67, 71, 73, 79, 89, 101, 109, 113, 127, 149, 151, 157, 167, 181, 191, 193, 197, 227, 257, 263, 271, 277, 281, 331, 347, 349, 379, 383, 431, 433, 449, 467, 479, 499, 509, 521, 523, 547, 563, 569, 571, 577, 587, 619, 631
Offset: 1

Views

Author

Vincenzo Librandi, Feb 05 2015

Keywords

Examples

			prime(5) = 11 is in the sequence because 11 + 6*5 = 41 is prime.
prime(8) = 19 is in the sequence because 19 + 6*8 = 67 is prime.

Links

Crossrefs

Cf. A061067, A231232, A231383, A254462, A254665, A254673.

Programs

  • Magma
    [NthPrime(n): n in [1..200] | IsPrime(NthPrime(n)+6*n)]
  • Mathematica
    Prime[Select[Range[150], PrimeQ[Prime[#] + 6 #] &]]

A254673 Primes prime(n) such that prime(n) + 4*n is also prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 23, 47, 59, 71, 73, 79, 97, 103, 113, 127, 137, 181, 199, 251, 263, 271, 281, 293, 331, 359, 367, 397, 419, 433, 443, 449, 457, 463, 487, 503, 523, 541, 571, 607, 613, 617, 631, 653, 709, 719, 751, 761, 773, 829, 839, 877, 881, 953, 967, 971
Offset: 1

Views

Author

Vincenzo Librandi, Feb 05 2015

Keywords

Examples

			prime(4)=7 is in the sequence because 7+4*4 = 23 is prime.
prime(6)=13 is in the sequence because 13+4*6 = 37 is prime.

Links

Crossrefs

Cf. A061067, A231232, A231383, A254462, A254665, A254672.

Programs

  • Magma
    [NthPrime(n): n in [1..200] | IsPrime(NthPrime(n)+4*n)]
  • Mathematica
    Prime[Select[Range[180], PrimeQ[Prime[#] + 4 #] &]]

A364877 Numbers k such that 2*pi(k) + k is a prime number.

Original entry on oeis.org

3, 5, 9, 17, 21, 23, 25, 31, 37, 41, 43, 45, 49, 57, 61, 65, 69, 85, 89, 91, 99, 103, 107, 109, 113, 119, 121, 129, 133, 135, 143, 151, 155, 159, 163, 165, 177, 185, 187, 191, 193, 195, 201, 213, 217, 219, 231, 235, 241, 243, 247, 251, 257, 267, 269, 273, 279
Offset: 1

Views

Author

Saish S. Kambali, Aug 11 2023

Keywords

Comments

All terms of this sequence are odd.
A231232 lists the prime terms of this sequence.

Examples

			k = 17 is a term: 2*pi(17) + 17 = 14 + 17 = 31, a prime number.

Links

Crossrefs

Cf. A000720, A231232.

Programs

  • Maple
    R:= NULL: count:= 0:
m:= 0:
for k from 1 while count < 100 do
  if isprime(k) then m:= m+1 fi;
  if isprime(2*m+k) then R:= R,k; count:= count+1 fi
od:
R; # Robert Israel, Oct 16 2023
  • Mathematica
    Select[Range[280], PrimeQ[2*PrimePi[#] + #] &] (* Amiram Eldar, Aug 11 2023 *)
  • PARI
    isok(k) = isprime(2*primepi(k) + k); \\ Michel Marcus, Aug 12 2023

Extensions

More terms from Jon E. Schoenfield, Aug 11 2023

A231332 Primes p = prime(k) such that p - 2k and p + 2k are prime.

Original entry on oeis.org

17, 23, 37, 89, 113, 151, 307, 463, 557, 643, 701, 761, 863, 911, 977, 1019, 1069, 1093, 1427, 1481, 1733, 1867, 2521, 2687, 2731, 2753, 3163, 3221, 3581, 3623, 3877, 4139, 4243, 4621, 4643, 4783, 4861, 4889, 4937, 5443, 5569, 5807, 5903, 6619, 6701, 6761, 6871
Offset: 1

Views

Author

Zak Seidov, Jan 07 2014

Keywords

Comments

Corresponding values of k: 7, 9, 12, 24, 30, 36, 63, 90, 102, 117, 126, 135, 150. All except the first one, 7, are multiples of 3.

Examples

			17 is the seventh prime, and 17 - 2 * 7 = 3 and 17 + 2 * 7 = 31, both of which are prime, so 17 is in the sequence.
23 is the ninth prime, and 23 - 2 * 9 = 5 and 23 + 2 * 9 = 41, both of which are prime, so 23 is in the sequence.
29 is the tenth prime, and 29 - 2 * 10 = 9 and 29 + 2 * 10 = 49, neither of which is prime, so 29 is not in the sequence.

Links

Crossrefs

Intersection of A231232 and A231326. Cf. A000040, A231506, A014689

Programs

  • Mathematica
    Reap[Sow[17]; Do[p = Prime[k]; If[PrimeQ[p + 2 * k] && PrimeQ[p - 2 * k], Sow[p]], {k, 9, 10^3, 3}]][[2, 1]]
Select[Table[{n, Prime[n]},{n,1000}],AllTrue[#[[2]]+{2#[[1]],-2#[[1]]},PrimeQ]&][[All,2]] (* Harvey P. Dale, Aug 05 2022 *)
  • PARI
    {print(17","); forstep(k=9,885,3,p=prime(k);if(isprime(p+2*k)&& isprime(p-2*k),print(p",")))}
  • PARI
    k=0;forprime(p=2,1e6,k++;if(isprime(p-2*k) && isprime(2+2*k), print1(p", "))) \\ Charles R Greathouse IV, Jan 07 2014

A231432 Primes p such that abs(p - 3*k) is also prime, where p is the k-th prime.

Original entry on oeis.org

3, 7, 13, 19, 31, 41, 47, 53, 61, 71, 79, 89, 101, 107, 113, 139, 151, 173, 193, 199, 223, 229, 239, 251, 271, 281, 293, 349, 373, 397, 433, 457, 463, 521, 541, 557, 569, 593, 601, 613, 619, 641, 647, 673, 683, 743, 787, 809, 839, 911, 941, 953, 971, 1013, 1049
Offset: 1

Views

Author

K. D. Bajpai, Nov 09 2013

Keywords

Examples

			The first prime, 2, is not a term since |2-3*1| = 1.
The second prime, 3, is a term, since |3-2*3| = 3 is a prime.
a(11) = 79 which is the 22nd prime, prime(22)-3*22 = 79-66 = 13 which is also prime.
a(15) = 113 which is the 30th prime, prime(30)-3*30 = 113-90 = 23 which is also prime.

Links

Crossrefs

Cf. A061068 (primes: prime(m) plus its subscript).
Cf. A064402 (numbers n: prime(n)+n is prime).
Cf. A231232 (primes p : p+2*k is also prime).
Cf. A231383 (primes p : p+3*k is also prime).

Programs

  • Maple
    KD := proc() local a, b;  a:= ithprime(n); b:= abs(a-3*n); if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..500);
  • Mathematica
    KD = Select[Table[{Prime[n], Prime[n] - 3*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[KD][[1]]
Select[Table[{k,Prime[k]},{k,200}],PrimeQ[Abs[#[[2]]-3#[[1]]]]&][[;;,2]] (* Harvey P. Dale, Jul 14 2024 *)
  • PARI
    k=0;forprime(p=2,1e3,if(isprime(abs(p-k++*3)), print1(p", "))) \\ Charles R Greathouse IV, Mar 11 2014
Showing 1-10 of 11 results. Next

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