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 1-4 of 4 results.

A101909 Number of primes between 2n and 4n.

Original entry on oeis.org

1, 2, 2, 2, 4, 4, 3, 5, 4, 4, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10, 9, 10, 9, 10, 12, 12, 13, 14, 13, 12, 13, 14, 13, 15, 14, 13, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 21, 20, 19, 20, 19, 18, 19, 19, 20, 21, 22, 23, 23, 24, 23, 24, 24, 24, 26, 25, 25, 27, 27, 27, 28, 27, 26
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Links

Crossrefs

Cf. A101947, A101983, A101984, A101985.

Programs

  • Maple
    A101909 := proc(n::integer)
    numtheory[pi](4*n)-numtheory[pi](2*n) ;
end proc:
seq(A101909(n),n=1..100) ; # R. J. Mathar, Oct 02 2019
  • Mathematica
    f[n_] := PrimePi[4n] - PrimePi[2n]; Table[ f[n], {n, 76}] (* Robert G. Wilson v, Feb 10 2005 *)
  • PARI
    bet2n4n(n) = { local(c,x,y); forstep(x=2,n,2, c=0; forprime(y=x+1,x+x-1, c++; ); print1(c",") ) }
  • PARI
    s=0;vector(100,n,s+=isprime(4*n-1)+isprime(4*n-3)-isprime(2*n-1)) \\ Charles R Greathouse IV, Mar 12 2012

Formula

a(n) = A099802(2*n)-A099802(n). - R. J. Mathar, Oct 02 2019

A101983 Numbers that do not occur in A101909 (= number of primes between 2n and 4n).

Original entry on oeis.org

11, 79, 134, 184, 186, 215, 245, 262, 284, 305, 387, 544, 694, 700, 706, 776, 814, 881, 939, 974, 1002, 1027, 1079, 1104, 1133, 1146, 1184, 1193, 1207, 1354, 1387, 1415, 1441, 1495, 1574, 1587, 1608, 1662, 1690, 1801, 1915, 1987, 2054, 2067, 2104, 2170
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Examples

			11 is the first number that does not equal a count of primes between 2n and 4n for some n.

Crossrefs

Complement of A101947.
Cf. A101909.

Programs

  • Mathematica
    f[n_] := PrimePi[4n] - PrimePi[2n]; t = Union[ Table[ f[n], {n, 12000}]]; Complement[ Range[ t[[ -1]]], t] (* Robert G. Wilson v, Feb 10 2005 *)
  • PARI
    bet2n4n(n)={ my( b=vecsort(vector(n, x, my(c=0); forprime(y=2*x+1,4*x-1, c++); c))); for(x=1,n-2, while(b[x+1]-b[x]>1,print1(b[x]++,",")))} \\ It's probably faster to use A101909 instead of forprime(...). Edited and corrected by M. F. Hasler, Sep 29 2019
  • PARI
    primecount(a,b)=primepi(b)-primepi(a);
v=vector(20000);
for(k=1,oo,j=primecount(2*k,4*k);if(j>#v,break,v[j]++));
for(k=1,2170,if(v[k]==0,print1(k,", "))) \\ Hugo Pfoertner, Sep 29 2019

Extensions

More terms from Robert G. Wilson v, Feb 10 2005
Name edited by M. F. Hasler, Sep 29 2019

A101984 Numbers that occur exactly once in A101909 (= count of primes between 2n and 4n).

Original entry on oeis.org

1, 3, 5, 8, 22, 36, 37, 46, 47, 48, 53, 63, 83, 98, 99, 101, 105, 108, 113, 114, 127, 135, 139, 148, 150, 155, 158, 171, 172, 173, 174, 175, 177, 178, 188, 205, 210, 218, 219, 220, 221, 226, 231, 240, 246, 254, 277, 282, 297, 298, 301, 303, 327, 333, 334, 339
Offset: 1

Views

Author

Cino Hilliard, Jan 28 2005

Keywords

Examples

			There are 5 primes between 16 and 32 and nowhere else between 2n and 4n.

Crossrefs

Cf. A101909, A101947, A101983, A101985.

Programs

  • PARI
    bet2n4n(n)={ my(b=vecsort(vector(n,x, my(c=0); forprime(y=2*x+1,4*x-1, c++); c))); print1(1","); for(x=1,n-2, if(b[x+1]>b[x] && b[x+1]Don Reble. - M. F. Hasler, Sep 29 2019

Extensions

Better name from N. J. A. Sloane, Sep 29 2019
Corrected a(22) and a(45), following an observation by Don Reble. - M. F. Hasler, Sep 29 2019

A337843 a(n) is n + the number of digits in the decimal expansion of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69
Offset: 0

Views

Author

Jaroslav Krizek, Sep 25 2020

Keywords

Comments

a(n) is an increasing injective sequence that is not surjective.
a(n) is also the sequence of numbers m that can be written as (m + number of digits of m) for some m >= 0, complement of numbers from A081552(n) for n > 1.
Sequence is not the same as A101947, first different term is a(77) = 79.

Examples

			a(10) = 10 + 2 = 12.

Crossrefs

Cf. A055642, A062028, A081552, A230099.
Cf. A110803 (n * the number of digits in the decimal expansion of n).

Programs

  • Magma
    [1] cat [n + #Intseq(n): n in [1..100]];
  • Mathematica
    a[0] = 1; a[n_] := n + IntegerLength[n]; Array[a, 100, 0] (* Amiram Eldar, Sep 25 2020 *)
  • PARI
    a(n) = if (n==0, 1, n + #digits(n)); \\ Michel Marcus, Sep 26 2020

Formula

a(n) = n + A055642(n).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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