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.

A050766 Primes occurring in A050765.

Original entry on oeis.org

38431, 59333, 89753, 93683, 156007, 356441, 682141, 1226959, 1468387, 1648697, 2592043, 2995249, 3595589, 3933731, 5845309, 5967433, 8861059, 8953631, 9748537, 11351399, 12819329, 13227023, 13712551, 16193579, 18375053, 19294523, 21206117, 25259593, 28297559
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Examples

			Prime 19294523 = composite 19294436 + sopf 2+2+7+7+7+7+7+7+41 = 19294436 + 87 = nextprime(19294436).

Links

Crossrefs

Cf. A050765, A050703, A050710.

Programs

  • Mathematica
    Reap[For[n = 4, n <= 2*10^7, n = If[PrimeQ[n+1], n+2, n+1], p = NextPrime[n]; If[n + Total[Times @@@ FactorInteger[n] ] == p, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 18 2013 *)

Extensions

Offset corrected by Donovan Johnson, Oct 18 2013

A105779 Numbers n such that n + (sum of prime factors of n) = next prime after n.

Original entry on oeis.org

24, 48, 54, 144, 288, 384, 648, 972, 1260, 1728, 1792, 1936, 1944, 2304, 3584, 5184, 6250, 6912, 7168, 8748, 8788, 9216, 9604, 10000, 10125, 10816, 11760, 13122, 13824, 17640, 21632, 21952, 23328, 24255, 25088, 26244, 27648, 33264, 35937, 37752
Offset: 1

Views

Author

Joseph L. Pe, May 06 2005

Keywords

Examples

			24 + (sum of prime factors of 24) = 24 + (2 + 3) = 29, the next prime after 24. So 24 belongs to the sequence.

Links

Crossrefs

Cf. A050765, A235425.

Programs

  • Mathematica
    Select[Range[2, 10^5], NextPrime[#] == # + Plus @@ First /@ FactorInteger@# &]
  • PARI
    sopf(n)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
is(n)=nextprime(n+1)-n==sopf(n) \\ Charles R Greathouse IV, Jan 10 2014

A235425 Numbers k such that between k and the next prime there are gpf(k) numbers, where gpf(k) denotes the largest prime factor of k.

Original entry on oeis.org

8, 64, 128, 625, 729, 1701, 2625, 3025, 4096, 6435, 8505, 10115, 12675, 14641, 17303, 19343, 19683, 19845, 21125, 25515, 25725, 26325, 26741, 27783, 32768, 33075, 33275, 34075, 35721, 38025, 39375, 42525, 43875, 50193, 59319, 60835, 61731, 70805, 75411, 75803
Offset: 1

Views

Author

Giovanni Resta, Jan 10 2014

Keywords

Examples

			64 = 2^6, whose largest prime factor is 2, is in the sequence because between 64 and 67 (the next prime) there are 2 numbers, 65 and 66.

Links

Crossrefs

Cf. A050765, A105779.

Programs

  • Mathematica
    Select[Range[10^5], NextPrime[#] - # == 1 + FactorInteger[#][[-1, 1]] &]
  • PARI
    gpf(n)=n=factor(n)[,1];n[#n]
is(n)=nextprime(n)-n==gpf(n)+1 \\ Charles R Greathouse IV, Jan 10 2014

A050777 First occurrence from iterated procedure 'composite k added to sum of its prime factors reaches a prime' yielding n skipped primes.

Original entry on oeis.org

38400, 6, 10, 26, 8, 18, 4, 39, 16, 30, 27, 32, 126, 76, 92, 87, 63, 77, 122, 49, 62, 120, 56, 50, 45, 117, 110, 196, 88, 102, 75, 246, 171, 72, 70, 234, 60, 469, 66, 217, 260, 198, 244, 387, 550, 230, 528, 362, 519, 764, 500, 494, 566, 376, 548, 386, 526, 481
Offset: 0

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Examples

			a(1)=38400 + (2+2+2+2+2+2+2+2+2+3+5+5) = 38431. '0' primes between 38400 and 38431.
a(2)=6 + (2+3) = 11. '1' prime between 6 and 11.
a(3)=10 + (2+5) = 17. '2' primes between 10 and 17.

Links

Crossrefs

Cf. A050765, A050768-A050776, A050703.

Programs

  • Mathematica
    a[n_]:=Length[Select[Range[n+1,NestWhile[#+Total[Times@@@FactorInteger[#]]&,n,!PrimeQ[#]&]-1],PrimeQ]]; t={38400}; Do[i=4; While[a[i]!=k,If[PrimeQ[i+1],i+=2,i++]]; AppendTo[t,i],{k,57}]; t (* Jayanta Basu, Jun 01 2013 *)
Showing 1-4 of 4 results.

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

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