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 1-6 of 6 results.

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 #] &]]

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 #] &]]

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 1-6 of 6 results.

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