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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A052299 Minimal number of distinct prime factors of any composite number between n-th and (n+1)-st primes.

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 3, 2, 3, 2, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 1, 1, 2, 2, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 4, 2, 2
Offset: 2

Views

Author

Labos Elemer, Feb 09 2000

Keywords

Examples

			For n = 81: prime(81) = 419, prime(82) = 421. The intermediate range of composites includes only 420 = 4*3*5*7 having 4 distinct prime factors, so a(81) = 4.

Links

Crossrefs

Cf. A052180, A052248, A052298.

Programs

  • Mathematica
    Min[PrimeNu[Range[#[[1]]+1,#[[2]]-1]]]&/@Partition[Prime[ Range[ 2,110]],2,1] (* Harvey P. Dale, Mar 31 2012 *)

Extensions

Offset corrected by Sean A. Irvine, Nov 04 2021

A069898 Smallest of the largest prime divisors of all the composite numbers between prime(n) and prime(n+1).

Original entry on oeis.org

2, 3, 2, 3, 2, 3, 5, 3, 5, 2, 5, 7, 5, 3, 3, 5, 2, 7, 3, 5, 3, 7, 3, 5, 17, 7, 3, 7, 5, 2, 5, 23, 3, 5, 11, 3, 11, 7, 7, 5, 7, 3, 7, 11, 5, 3, 5, 19, 11, 13, 5, 3, 2, 13, 11, 5, 11, 7, 47, 3, 5, 11, 13, 7, 3, 7, 7, 29, 7, 17, 5, 23, 5, 19, 3, 7, 5, 5, 13, 7, 13, 3, 23, 7, 7, 5, 17, 11, 29, 13, 3, 7
Offset: 2

Views

Author

Labos Elemer, Apr 10 2002

Keywords

Examples

			n=128: prime(128) = 719, prime(129) = 727, d = 8; composites between the 2 primes:{720,721,722,723,724,725,726}; factor-sets: (2,3,5),(7,103),(2,19),(3,241),(2,3,181),(5,29),(2,3,11), least factors:{2,7,2,3,2,5,2};  Min and Max = {2,7}; largest factors:{5,103,241,181,29,11}; Min and Max = {5,241}; max-of-least = A052180(128) = 7, max-of-largest = A052248(128) = 241, a(128) = min-of-largest = a(128) = 5.

Links

Crossrefs

Cf. A020639, A006530, A052180, A052248.

Programs

  • Mathematica
    ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}]; mif[x_] := Min[ba[x]]; maf[x_] := Max[ba[x]]; Table[Min[Table[maf[w], {w, Prime[n]+1, Prime[n+1]-1}]], {n, 1, 128}]
  • PARI
    lista(plim) = {my(pmin, prev = 3); forprime(p = 5, plim, pmin = p; for(k = prev+1, p-1, pmin = min(pmin, vecmax(factor(k)[, 1]))); print1(pmin, ", "); prev = p);} \\ Amiram Eldar, Oct 24 2024

A079602 Greatest of smallest odd prime factors of all composite numbers between n-th prime and next prime.

Original entry on oeis.org

3, 5, 3, 7, 3, 11, 13, 3, 17, 19, 3, 23, 13, 29, 3, 31, 17, 3, 37, 41, 43, 47, 7, 3, 53, 3, 7, 61, 5, 67, 3, 73, 3, 19, 79, 83, 43, 89, 3, 47, 3, 97, 3, 103, 109, 113, 3, 29, 59, 3, 61, 127, 131, 67, 3, 137, 139, 3, 73, 151, 7, 3, 157, 163, 167, 173, 3, 11, 179, 181, 23, 47, 191
Offset: 3

Views

Author

Reinhard Zumkeller, Jan 28 2003

Keywords

Links

Crossrefs

Cf. A078701, A052180.

Programs

  • Mathematica
    a[n_] := Max[FactorInteger[#/2^IntegerExponent[#, 2]][[1, 1]] & /@ Range[Prime[n] + 1, Prime[n + 1] - 1]]; Array[a, 100, 3] (* Amiram Eldar, Mar 28 2025 *)
Previous Showing 21-23 of 23 results.

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

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