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 1-3 of 3 results.

A261701 Initial member of four twin prime pairs with gap 210 between them.

Original entry on oeis.org

599, 3917, 5021, 37361, 48779, 81929, 93281, 97157, 263399, 433049, 783149, 821801, 906119, 908669, 1197197, 1308497, 1308707, 1379237, 1464809, 1908449, 2036861, 2341979, 2408561, 2760671, 2804309, 3042491, 3042701, 3042911, 3198197, 4090649, 4543991, 5543927
Offset: 1

Views

Author

K. D. Bajpai, Aug 28 2015

Keywords

Comments

More precisely, primes p such that p + 2, p + 210, p + 212, p + 420, p + 422, p + 630, p + 632 are all primes.
All the terms in this sequence are congruent to 2 (mod 3).

Examples

			599 appears in the sequence because: (a) {599,601}, {809, 811}, {1019, 1021}, {1229, 1231} are four (not consecutive) twin prime pairs; (b) the gap between each twin prime pair (809 - 599) = (1019 -  809) = (1229 - 1019) = 210.

Links

Crossrefs

Cf. A001359 (twin primes), A077800, A113274, A253624.

Programs

  • Magma
    [p: p in PrimesUpTo (100000) | IsPrime(p+2) and IsPrime(p+210) and IsPrime(p+212) and IsPrime(p+420) and IsPrime(p+422) and IsPrime(p+630) and IsPrime(p+632) ];
  • Maple
    select(p -> andmap(isprime, [p, p+2, p+210, p+212, p+420, p+422, p+630, p+632]),[seq(p, p=1..10^5)]);
  • Mathematica
    k = 210; Select[Prime@Range[10^7], PrimeQ[# + 2] && PrimeQ[# + k] && PrimeQ[# + k + 2] && PrimeQ[# + 2 k] && PrimeQ[# + 2 k + 2] && PrimeQ[# + 3 k] &&  PrimeQ[# + 3 k + 2] &]
Select[Prime[Range[400000]],AllTrue[#+{2,210,212,420,422,630,632},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 17 2019 *)
  • PARI
    forprime(p= 1, 100000, if(isprime(p+2) && isprime(p+210) && isprime(p+212) && isprime(p+420) && isprime(p+422) && isprime(p+630) && isprime(p+632), print1(p,", ")));
  • Perl
    use ntheory ":all"; say join ", ", grep { is_prime($+210) && is_prime($+212) && is_prime($+420) && is_prime($+422) && is_prime($+630) && is_prime($+632) } @{twin_primes(1e8)}; # Dana Jacobsen, Sep 02 2015
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(1, 1e8, 2, 210, 212, 420, 422, 630, 632); # Dana Jacobsen, Oct 03 2015

A245568 Initial members of prime quadruples (n, n+2, n+24, n+26).

Original entry on oeis.org

5, 17, 617, 857, 1277, 1427, 1697, 2087, 2687, 3557, 4217, 5417, 5477, 7307, 8837, 9437, 10067, 13877, 17657, 18287, 20747, 21587, 23537, 25577, 27917, 28547, 30467, 32117, 32297, 35507, 37337, 37547, 40127, 41177, 41387, 41957
Offset: 1

Views

Author

Karl V. Keller, Jr., Jan 09 2015

Keywords

Comments

This sequence is prime n, where there exist two twin prime pairs of (n, n+2, n+24, n+26).
Excluding 5, this is a subsequence of each of the following: A128468 (a(n) = 30*n + 17), A039949 (Primes of the form 30n-13), A181605 (twin primes ending in 7).
A253624 is a subsequence of this sequence.

Examples

			For n = 17, the numbers 17, 19, 41, 43 are primes.

Links

Crossrefs

Cf. A077800 (twin primes), A128468, A039949, A181605, A253624.

Programs

  • Mathematica
    a245568[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 24], PrimeQ[# + 26]] &]; a245568[5000] (* Michael De Vlieger, Jan 11 2015 *)
  • Python
    from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+24) and isprime(n+26): print(n,end=', ')

A261731 Initial member of five twin prime pairs with gap 210 between them.

Original entry on oeis.org

1308497, 3042491, 3042701, 7445309, 20031101, 31572521, 44687987, 54266291, 141208619, 182316521, 237416369, 357080021, 448436321, 611641187, 699458411, 761126027, 774997367, 794065967, 836452961, 915215591, 944958941, 1009194617, 1581935939, 1763255561, 1871007371
Offset: 1

Views

Author

K. D. Bajpai, Aug 30 2015

Keywords

Comments

More precisely, primes p such that p+2, p+210, p+212, p+420, p+422, p+630, p+632, p+840, p+842 are all primes.
All the terms in this sequence are congruent to 2 (mod 3).

Examples

			1308497 appears in this sequence because: (a) {1308497, 1308499}, {1308707, 1308709}, {1308917, 1308919}, {1309127, 1309129}, and {1309337, 1309339} are five twin prime pairs; (b) the gap between each twin prime pair {1308707 - 1308497} = {1308917-1308707} = {1309127 - 1308917} = {1309337 - 1309127} = 210.

Links

Crossrefs

Cf. A077800, A113274, A253624, A261701.

Programs

  • Magma
    [p: p in PrimesUpTo (100000) | IsPrime(p+2) and IsPrime(p+210) and IsPrime(p+212) and IsPrime(p+420) and IsPrime(p+422) and IsPrime(p+630) and IsPrime(p+632) and IsPrime(p+840) and IsPrime(p+842) ];
  • Maple
    select(p -> andmap(isprime, [p, p+2, p+210, p+212, p+420, p+422, p+630, p+632, p+840, p+842]),[seq(p, p=1..2*10^7)]);
  • Mathematica
    k = 210; Select[Prime@Range[6*10^7], PrimeQ[# + 2] && PrimeQ[# + k] && PrimeQ[# + k + 2] && PrimeQ[# + 2 k] && PrimeQ[# + 2 k + 2] && PrimeQ[# + 3 k] &&   PrimeQ[# + 3 k + 2] && PrimeQ[# + 4 k] && PrimeQ[# + 4 k + 2] &]
Select[Prime[Range[93*10^6]],AllTrue[#+{2,210,212,420,422,630,632,840,842},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 05 2018 *)
  • PARI
    forprime(p= 1,3*10^9, if(isprime(p+2) && isprime(p+210) && isprime(p+212) && isprime(p+420) && isprime(p+422) && isprime(p+630) && isprime(p+632) && isprime(p+840) && isprime(p+842), print1(p,", ")));
  • Perl
    use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2, 210, 212, 420, 422, 630, 632, 840, 842); # Dana Jacobsen, Oct 02 2015
Showing 1-3 of 3 results.

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