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.

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A336966 Primes starting 10-tuples of consecutive primes that have symmetrical gaps about their mean and form 5 pairs of twin primes.

Original entry on oeis.org

3031329797, 5188151387, 14168924459, 14768184029, 18028534367, 26697800819, 26919220961, 29205326387, 32544026699, 39713433671, 45898528799, 48263504459, 50791655009, 66419473031, 71525244611, 80179195037, 83700877199, 86767580069, 97660776137, 108116163479
Offset: 1

Views

Author

Tomáš Brada, Aug 09 2020

Keywords

Examples

			a(1) = A274792(5) = 3031329797 starts a 10-tuple of consecutive primes: 3031329797+s for s in {0, 2, 12, 14, 42, 44, 72, 74, 84, 86} that are symmetric about 3031329797+43 and form 5 pairs of twin primes.
		

Crossrefs

A333977 Prime starting a sequence of 20 consecutive primes with symmetrical gaps about the center.

Original entry on oeis.org

1797595814863, 2375065608481, 4465545586753, 21818228348093, 67696772430071, 82116093014611, 155947272322087, 161980267642951, 169560139541641, 202619277419161, 285719200081877, 299828814652799, 314942862282899, 365706921997577
Offset: 1

Views

Author

Tomáš Brada, Sep 20 2020

Keywords

Crossrefs

Formula

Primes p = prime(k) = A000040(k) such that A359440(k+9) >= 9. - Peter Munn, Jan 09 2023

A263171 Smallest prime starting a sequence of 4 consecutive odd primes such that the center of the symmetrical gaps is 2n.

Original entry on oeis.org

7, 5, 251, 353, 137, 2393, 109, 1931, 1753, 883, 3733, 7351, 12007, 2969, 8887, 27697, 1321, 22811, 38377, 62987, 183823, 15679, 124001, 180563, 45887, 48677, 100847, 178693, 152993, 557087, 34057, 367949, 294551, 134507, 173357, 1802407, 531359, 1134311, 933067
Offset: 1

Views

Author

Michel Lagneau, Oct 11 2015

Keywords

Comments

The sequence is generalizable with primes starting a sequence of 2k consecutive odd primes.
Conjecture: a(n) exists for all n>0.

Examples

			a(2)=5 because the 4 consecutive primes 5, 7, 11, 13 have gaps 2, 4, 2, which is symmetric about its center 4 = 2*2.
		

Crossrefs

Programs

  • Maple
    with(numtheory):nn:=500000:l:=2:T:=array(1..2*l-1)):
    for n from 1 to 35 do:ii:=0:
      for k from 1 to nn while(ii=0) do:
          lst:={}:lst1:={}:
           for m from 1 to 2*l do:
            lst:=lst union {ithprime(k+m-1)}
           od:
             for p from 1 to 2*l do:
              lst1:=lst1 union {lst[p]+lst[2*l-p+1]}
             od:
                n0:=nops(lst1):
                if n0=1
                then
               for a from 1 to 2*l-1 do:
               T[a]:=lst[a+1]-lst[a]:
               od:
               if T[2]=2*n then ii:=1:printf(`%d, `,lst[1]):
               else fi :fi:
               od :
              od:
  • PARI
    a(n) = {pa = 3; pb = 5; pc = 7; forprime(p=8, , if (((pc-pb) == 2*n) && ((pb-pa) == (p-pc)), return(pa)); pa = pb; pb = pc; pc = p;);} \\ Michel Marcus, Oct 16 2015
Previous Showing 11-13 of 13 results.