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 1-7 of 7 results.

A127558 Decimal expansion of the number 29.000694926917980144237135814... having continued fraction expansion 29, 1439, 4211, 7703, 12907, 14957, ... (A126555).

Original entry on oeis.org

2, 9, 0, 0, 0, 6, 9, 4, 9, 2, 6, 9, 1, 7, 9, 8, 0, 1, 4, 4, 2, 3, 7, 1, 3, 5, 8, 1, 4, 0, 8, 7, 8, 4, 9, 1, 2, 0, 4, 8, 7, 4, 8, 2, 8, 7, 5, 9, 7, 5, 7, 3, 4, 7, 7, 9, 8, 4, 2, 5, 9, 3, 4, 4, 6, 1, 5, 1, 6, 0, 6, 4, 5, 0, 8, 6, 1, 3, 6, 3, 8, 3, 5, 5, 3, 0, 0, 3, 0, 9, 5, 0, 0, 9, 6, 7, 2, 9, 5, 6
Offset: 2

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127559, A126555.

Programs

  • Mathematica
    b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 100000}];Do[If[PrimeQ[(a[[k + 1]] + a[[k]])/2], AppendTo[b, (a[[k + 1]] + a[[k]])/2]], {k, 1, Length[a] - 1}]; RealDigits[N[FromContinuedFraction[b], 100]][[1]]

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

A126554 Arithmetic mean of two consecutive balanced primes (of order one).

Original entry on oeis.org

29, 105, 165, 192, 234, 260, 318, 468, 578, 600, 630, 693, 840, 962, 1040, 1113, 1155, 1205, 1295, 1439, 1629, 1750, 1830, 2097, 2352, 2547, 2790, 2933, 3135, 3310, 3475, 3685, 3873, 4211, 4433, 4527, 4627, 4674, 4842, 5050, 5110, 5208, 5345, 5390, 5478
Offset: 1

Views

Author

Artur Jasinski, Dec 27 2006

Keywords

Comments

Might be called interprimes of order two, since the arithmetic means of two consecutive odd primes (A024675) sometimes are called interprimes.
Balanced primes of order two (A082077) and doubly balanced primes (A051795) have different definitions.
For primes in this sequence (prime interprimes of order two) see A126555.

Links

Crossrefs

Cf. A006562, A024675, A082077, A051795, A126555.

Programs

  • GAP
    P:=Filtered([1..6000],IsPrime);;P1:=List(Filtered(List([0..Length(P)-3],k->List([1..3],j->P[j+k])),i->Sum(i)/3=i[2]),m->m[2]);;
a:=List([1..Length(P1)-1],n->(P1[n+1]+P1[n])/2); # Muniru A Asiru, Mar 31 2018
  • Mathematica
    b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 1000}]; Do[AppendTo[b, (a[[k + 1]] + a[[k]])/2], {k, 1, Length[a] - 1}]; b
  • PARI
    {m=6000;a=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,print1((a+q)/2,","));a=q);p=q;q=r;r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 05 2007

Formula

a(n) = (A006562(n+1)+A006562(n))/2.

Extensions

Edited by Klaus Brockhaus, Jan 05 2007

A126556 Arithmetic mean of two consecutive prime interprimes of second order: interprimes of third order.

Original entry on oeis.org

734, 2825, 5957, 10305, 13932, 15830, 18825, 25084, 30205, 32121, 34901, 40640, 47984, 70842, 102897, 120165, 125973, 130250, 138924, 145480, 148894, 154236, 161676, 167730, 174737, 180632, 183077, 191253, 210375, 224327, 232817, 246285
Offset: 1

Views

Author

Artur Jasinski, Dec 27 2006

Keywords

Comments

For primes in this sequence (prime interprimes of third order) see A126557.

Links

Crossrefs

Cf. A006562 (balanced primes), A024675 (interprimes), A126554 (interprimes of second order), A126555 (prime interprimes of second order).

Programs

  • PARI
    {m=250000;a=0;g=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,b=(a+q)/2;if(isprime(b),if(g>0,print1(h=(g+b)/2,","));g=b));a=q);p=q;q=r;r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 11 2007

Formula

a(n) = (A126555(n)+A126555(n+1))/2.

Extensions

Edited by Klaus Brockhaus, Jan 11 2007

A127559 Decimal expansion of the number 734.000353982279850297391846... having continued fraction expansion 734, 2825, 5957, 10305, 13932, ... (interprimes of third order A126556).

Original entry on oeis.org

7, 3, 4, 0, 0, 0, 3, 5, 3, 9, 8, 2, 2, 7, 9, 8, 5, 0, 2, 9, 7, 3, 9, 1, 8, 4, 6, 1, 5, 9, 2, 7, 6, 9, 4, 9, 1, 1, 2, 4, 7, 3, 4, 1, 2, 2, 3, 9, 9, 1, 6, 1, 1, 5, 8, 1, 5, 8, 2, 6, 1, 8, 9, 2, 4, 0, 3, 1, 3, 6, 2, 0, 9, 5, 9, 1, 6, 3, 9, 3, 0, 9, 5, 9, 1, 7, 9, 4, 0, 9, 5, 2, 7, 0, 5, 4, 2, 8, 2, 5
Offset: 3

Views

Author

Artur Jasinski, Jan 18 2007

Keywords

Crossrefs

Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127558, A127559, A126555, A126556.

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

A126557 Primes in A126556.

Original entry on oeis.org

174737, 224327, 433813, 541447, 787243, 969667, 980081, 1080787, 1286581, 1372979, 1534513, 1567037, 1570649, 1577189, 1659673, 1726993, 1931291, 2242883, 2282041, 2415557, 2460827, 3162503, 3711047, 4090787, 4450373
Offset: 1

Views

Author

Artur Jasinski, Dec 27 2006

Keywords

Comments

Prime interprimes of third order.
Primes that are the arithmetic mean of two consecutive prime interprimes of second order; primes of the form (A126555(k)+A126555(k+1))/2.

Links

Crossrefs

Cf. A006562 (balanced primes), A024675 (interprimes), A126554 (interprimes of second order), A126555 (prime interprimes of second order), A126556 (interprimes of third order).

Programs

  • PARI
    {m=5000000;a=0;g=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,b=(a+q)/2;if(isprime(b),if(g>0,if(isprime(h=(g+b)/2),print1(h,",")));g=b));a=q);p=q;q=r; r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 11 2007

Extensions

Edited and extended by Klaus Brockhaus, Jan 11 2007

A126558 Arithmetic mean of two consecutive prime interprimes of third order: interprimes of fourth order.

Original entry on oeis.org

199532, 329070, 487630, 664345, 878455, 974874, 1030434, 1183684, 1329780, 1453746, 1550775, 1568843, 1573919, 1618431, 1693333, 1829142, 2087087, 2262462, 2348799, 2438192, 2811665, 3436775, 3900917, 4270580, 4830665
Offset: 1

Views

Author

Artur Jasinski, Dec 27 2006

Keywords

Comments

For primes in this sequence (prime interprimes of fourth order) see A127364.

Links

Crossrefs

Cf. A006562 (balanced primes), A024675 (interprimes), A126554 (interprimes of second order), A126555 (prime interprimes of second order), A126556 (interprimes of third order), A126557 (prime interprimes of third order).

Programs

  • PARI
    {m=5000000;a=0;g=0;e=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,b=(a+q)/2;if(isprime(b),if(g>0,h=(g+b)/2;if(isprime(h),if(e>0,f=(e+h)/2;print1(f,","));e=h));g=b));a=q);p=q;q=r;r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 11 2007

Formula

a(n) = (A126557(n)+A126557(n+1))/2.

Extensions

Edited and extended by Klaus Brockhaus, Jan 11 2007

A127364 Primes in A126558.

Original entry on oeis.org

1693333, 14251277, 17306687, 18067739, 25852399, 29126567, 55781581, 62333321, 113347009, 173863769, 204308891, 211281809, 247612801, 256102939, 267030149, 267670129, 277108457, 291010691, 298502489, 337176617, 365570923, 370598051
Offset: 1

Views

Author

Klaus Brockhaus, Jan 11 2007

Keywords

Comments

Prime interprimes of fourth order.
Primes that are the arithmetic mean of two consecutive prime interprimes of third order; primes of the form (A126557(k)+A126557(k+1))/2.

Links

Crossrefs

Cf. A006562 (balanced primes), A024675 (interprimes), A126554 (interprimes of second order), A126555 (prime interprimes of second order), A126556 (interprimes of third order), A126557 (prime interprimes of third order), A126558 (interprimes of fourth order).

Programs

  • PARI
    {m=400000000;a=0;g=0;e=0;p=2;q=3;r=5;while(r<=m,if((p+r)/2==q,if(a>0,b=(a+q)/2;if(isprime(b),if(g>0,h=(g+b)/2;if(isprime(h),if(e>0,f=(e+h)/2;if(isprime(f),print1(f,",")));e=h));g=b));a=q);p=q;q=r;r=nextprime(r+1))}
Showing 1-7 of 7 results.

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