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.

Previous Showing 31-35 of 35 results.

A050775 Iterated procedure 'composite k added to sum of its prime factors reaches a prime' yields 8 skipped primes.

Original entry on oeis.org

16, 36, 74, 80, 81, 86, 115, 119, 121, 123, 141, 215, 266, 276, 360, 451, 465, 572, 779, 868, 1548, 1624, 1674, 1763, 1917, 1925, 2196, 2331, 2368, 2730, 3108, 3306, 3430, 3816, 4452, 4575, 5110, 5312, 5412, 6273, 6324, 6820, 7632, 8772, 9027, 9204, 9435
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1999

Keywords

Examples

			a(6)=86 + (2+43) = ending prime 131. Between 86 and 131 one finds 8 primes 89, 97, 101, 103, 107, 109, 113 and 127.

Crossrefs

Cf. A050703, A050710.

Extensions

Offset corrected by Sean A. Irvine, Aug 18 2021

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 *)

A057874 Sets of three composites in bidirectional 'sum of prime factors' progression/retrogression.

Original entry on oeis.org

95, 119, 143, 174191, 175031, 175871, 298687992, 298688708, 298689424
Offset: 0

Views

Author

Patrick De Geest, Sep 15 2000

Keywords

Comments

First term of next set > 2000000000.

Examples

			First set is (95,119,143) all terms having 'sum of prime factors' = 24. So '95' + (5+19) = '119' + (7+17) = '143' AND '143' - (11+13) = '119' - (7+17) = '95'.

Links

Crossrefs

Cf. A050780, A050781, A050703-A050710.

Extensions

This really seems to be three sequences, not one! Should be split. - N. J. A. Sloane

A177791 Partial sums of A050705.

Original entry on oeis.org

10, 22, 36, 51, 71, 92, 118, 151, 186, 224, 268, 316, 367, 432, 500, 586, 679, 775, 886, 998, 1114, 1237, 1398, 1586, 1787, 1990, 2196, 2405, 2615, 2830, 3051, 3329, 3626, 3926, 4230, 4536, 4857, 5209, 5565, 5936, 6320, 6715, 7113, 7526, 7946, 8387, 8858
Offset: 1

Views

Author

Jonathan Vos Post, May 13 2010

Keywords

Comments

Partial sums of composite number such that when sum of its prime factors is added or subtracted becomes prime. The subsequence of primes in the partial sums begins: 71, 151, 367, 1237, 1787, 3329, 5209, 8387, 9343, 13781. The subsequence of partial sums which are themselves composite number such that when sum of their prime factors is added or subtracted becomes prime, begins: 10, 51, which other such fixed points are there?

Examples

			a(13) = 10 + 12 + 14 + 15 + 20 + 21 + 26 + 33 + 35 + 38 + 44 + 48 + 51 = 367 is prime.

Crossrefs

Cf. A000040, A001414, A050705, A050703-A050710.

Formula

a(n) = SUM[i=1..n] A050705(i) = SUM[i=1..n] {n such that n+A001414(n) is in A000040, and n-A001414(n) is in A000040}.

A226218 Ending primes for n-th composite number in the iterated procedure of composite added to sum of prime factors.

Original entry on oeis.org

23, 11, 23, 23, 17, 19, 23, 23, 47, 41, 29, 31, 47, 47, 47, 41, 71, 71, 71, 83, 47, 53, 47, 71, 59, 71, 71, 83, 59, 167, 71, 59, 149, 167, 71, 167, 83, 71, 167, 79, 89, 251, 167, 149, 149, 83, 269, 89, 167, 251, 251, 113, 239, 149, 167, 109, 127, 269, 251, 107
Offset: 1

Views

Author

Jayanta Basu, May 31 2013

Keywords

Comments

If we consider nonprimes instead of composite then a(1)=2. Sorted list of primes generated here are given in A050778.

Examples

			For the first composite number 4 repeated application of composite added to sum of prime factors give 4, 8, 14, 23 and so a(1)=23.

Crossrefs

Cf. A050703-A050710, A050778.

Programs

  • Mathematica
    a[n_] := NestWhile[#+Total[Times@@@FactorInteger[#]]&, n, !PrimeQ[#]&]; t={}; Do[If[!PrimeQ[n], AppendTo[t, a[n]]], {n, 4, 80}]; t
Previous Showing 31-35 of 35 results.

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

Content is available under The OEIS End-User License Agreement.