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 1-10 of 17 results. Next

A143717 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (abs(1-2-3, 2-2-5, 2-3-7, 2-3-3, 2-2-5, 11-2-2, 3-13-2, 7-3-5,..)).

Original entry on oeis.org

4, 5, 8, 4, 5, 7, 12, 1, 19, 3, 15, 5, 32, 4, 1, 7, 7, 24, 28, 9, 20, 3, 36, 20, 8, 38, 47, 11, 4, 68, 5, 3, 0, 13, 42, 5, 6, 15, 86, 3, 58, 26, 1, 10, 75, 17, 22, 73, 4, 73, 29, 2, 1, 14, 73, 2, 122, 3, 15, 44, 24, 80, 4, 8, 24, 18, 16, 95, 7, 10, 5, 101, 117, 14, 9, 158, 3, 108, 9, 31
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			Abs (7-3-5)=abs (-1) =1=a(8).
Abs (2-4-17)=abs(-19)=19=a(9).
Abs (2-3-2)=abs (-3)=3=a(10).
Abs (19-2-2)=abs 15=15=a(11),
Abs (5-3-7)=abs (-5)=5=a(12),
etc.

Crossrefs

Cf. A141287, A141261, A136678.

Extensions

Replaced a 56 by a 1. R. J. Mathar, Feb 21 2009

A143716 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,..) becomes (1, 2, 3, 4, 5^6, 7, 8*9, 10, 11^12, 13^14, 15*16, 17, 18^19*20,..).

Original entry on oeis.org

1, 2, 3, 4, 15625, 7, 72, 10, 313842837672, 393737638569928, 240, 17, 14164706907106753527152640
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Comments

The list of the bases and exponents of the prime factorizations is replaced by the list of positive integers, but the operations stay fixed. - R. J. Mathar, Mar 22 2016

Examples

			a(5)=5^6=15625.
a(6)=7.
a(7)=8*9=72.

Crossrefs

Cf. A141287, A141261, A136611.

Extensions

Definition and terms corrected. - R. J. Mathar, Mar 22 2016

A141186 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) becomes (2, 3, 5, 7^11, 13, 17*19, 23, 29^31, 37^41, 41*43, 53, 59^61*67, ...).

Original entry on oeis.org

2, 3, 5, 1977326743, 13, 323, 23, 2159424054808578564166497528588784562372597429, 19782022283855446341112457192300036270147066771005176357387103237, 2021
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 08 2008

Keywords

Examples

			a(5)=7^11=1977326743.
a(7)=17*19=323,
etc.

Crossrefs

Cf. A141287, A141261, A143678.

Extensions

More terms from R. J. Mathar, Apr 14 2010

A143710 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1+2+3, 2+2+5, 2+3+7, 2+3+3, 2+2+5, 11+2+2, 3+13+2, 7+3+5,..).

Original entry on oeis.org

6, 9, 12, 8, 9, 15, 18, 15, 23, 7, 23, 15, 36, 8, 9, 19, 11, 34, 38, 19, 24, 11, 42, 24, 18, 48, 53, 15, 10, 72, 9, 11, 10, 21, 68, 11, 16, 29, 90, 7, 68, 36, 15, 20, 81, 21, 28, 83, 8, 77, 45, 6, 37, 18, 85, 12, 126, 7, 29, 48, 34, 102, 10, 22, 28, 80, 26, 105, 11, 16, 9, 105, 123
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7+3+5=15.
a(9)=2+4+17=23.
a(10)=2+3+2=7.
a(11)=19+2+2=23.
a(12)=5+3+7=15.
a(13)=2+11+23=36,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

a(43) corrected by R. J. Mathar, Apr 14 2010

A143677 ( 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (abs (1-2, 3-2, 2-5, 2-3, 7-2, 3-3, 2-2, 5-11, 2-2, 3-13,..)).

Original entry on oeis.org

1, 1, 3, 1, 5, 0, 0, 6, 0, 10, 5, 2, 2, 15, 1, 17, 3, 4, 9, 21, 0, 3, 11, 0, 0, 22, 1, 26, 3, 8, 15, 2, 0, 1, 35, 16, 11, 2, 39, 4, 41, 9, 1, 3, 24, 2, 4, 0, 3, 14, 0, 40, 1, 2, 9, 4, 16, 27, 57, 1, 56, 29, 1, 5, 1, 11, 8, 65, 15, 20, 3, 64, 1, 1, 71, 34, 3, 0, 12, 9, 10, 77, 1, 1, 39, 81, 1, 2, 15
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 01 2008

Keywords

Examples

			Abs(1-2)=abs(-1)=1=a(1).
Abs(3-2)=abs(1)=1=a(2).
Abs(2-5)=abs(-3)=3=a(3).
Abs(2-3)=abs(-1)=1=a(4).
Abs(7-2)=abs(5)=5=a(5).
Abs(3-3)=abs(0)=0=a(6).
Abs(2-2)=abs(0)=0=a(7).
Abs(5-11)=abs(-6)=6=a(8).
Abs(2-2)=abs(0)=0=a(9).
Abs(3-13)=abs(-10)=10=a(10), etc.

Crossrefs

Cf. A141257, A141261.

Programs

  • Maple
    pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do a := [op(a),op(1,p)] ; if op(2,p) > 1 then a := [op(a),op(2,p)] ; fi; od: od: a ; end: pL := pflat2(300) : for n from 1 to nops(pL)-3 by 2 do printf("%d,", abs(op(n, pL)-op(n+1, pL)) ) ; od: # R. J. Mathar, Nov 06 2008

Extensions

Removed incompatibilities with internal OEIS format, extended, R. J. Mathar, Nov 06 2008

A143678 ( 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (abs (1-2+3, 2-2+5, 2-3+7, 2-3+3, 2-2+5, 11-2+2, 3-13+2, 7-3+5,..)).

Original entry on oeis.org

2, 5, 6, 2, 5, 11, 8, 9, 15, 1, 19, 9, 14, 2, 5, 13, 7, 30, 24, 13, 10, 7, 38, 14, 14, 34, 39, 11, 6, 26, 1, 7, 6, 17, 38, 5, 12, 23, 32, 3, 54, 30, 11, 6, 59, 17, 18, 69, 2, 69, 39, 2, 23, 12, 81, 6, 44, 3, 19, 38, 30, 76, 6, 4, 18, 76, 12, 99, 3, 12, 5, 97, 89, 12, 5, 56, 3, 104, 3, 39, 104, 11, 23, 28, 70, 8, 5, 11, 99, 31, 4, 8
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 01 2008

Keywords

Examples

			Abs(1-2+3)=abs(2)=2=a(1).
Abs(2-2+5)=abs(5)=5=a(2).
Abs(2-3+7)=abs(6)=6=a(3).
Abs(2-3+3)=abs(2)=2=a(4).
Abs(2-2+5)=abs(5)=5=a(5).
Abs(11-2+2)=abs(11)=11=a(6).
Abs(3-13+2)=abs(-8)=8=a(7).
Abs(7-3+5)=abs(9)=9=a(8), etc.

Crossrefs

Cf. A141257, A141261.

Programs

  • Maple
    pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do a := [op(a),op(1,p)] ; if op(2,p) > 1 then a := [op(a),op(2,p)] ; fi; od: od: a ; end:
pL := pflat2(300) : for n from 1 to nops(pL)-4 by 3 do printf("%d,", abs(op(n, pL)-op(n+1, pL)+op(n+2,pL)) ) ; od: # R. J. Mathar, Nov 06 2008

Extensions

Removed incompatibilities with internal OEIS format, extended R. J. Mathar, Nov 06 2008

A143704 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5, ...) becomes ((1+2)*3, (2+2)*5, (2+3)*7, (2+3)*3, (2+2)*5, (11+2)*2, (3+13)*2, (7+3)*5, ...).

Original entry on oeis.org

9, 20, 35, 15, 20, 26, 32, 50, 102, 10, 42, 56, 299, 15, 14, 48, 28, 93, 72, 88, 95, 18, 185, 63, 45, 92, 430, 44, 25, 1175, 18, 18, 21, 38, 132, 30, 39, 190, 1829, 12, 132, 68, 54, 36, 938, 68, 52, 852, 15, 150, 200, 8, 286, 65, 324, 32, 3569, 12, 204, 135, 93, 200, 25, 40
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)  = ( 7 +  3) *  5 = 10*5 = 50;
a(9)  = ( 2 +  4) * 17 = 102;
a(10) = ( 2 +  3) *  2 =  10;
a(11) = (19 +  2) *  2 =  42;
a(12) = ( 5 +  3) *  7 =  56;
a(13) = ( 2 + 11) * 23 = 199;
etc.

Links

Crossrefs

Cf. A141287, A141261, A136735.

Programs

  • Maple
    g:= proc(n) local L; L:= sort(ifactors(n)[2],(s,t) -> s[1]Robert Israel, Nov 16 2019

Extensions

Corrected (199 replaced by 299, 60 replaced by 30, 549 replaced by 54 etc.) by R. J. Mathar, Apr 18 2010

A143711 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1*2*3, 2*2*5, 2*3*7, 2*3*3, 2*2*5, 11*2*2, 3*13*2, 7*3*5,..).

Original entry on oeis.org

6, 20, 42, 18, 20, 44, 78, 105, 136, 12, 76, 105, 506, 18, 20, 117, 28, 174, 310, 165, 170, 28, 222, 114, 78, 410, 903, 44, 30, 2162, 24, 28, 30, 68, 1378, 45, 66, 399, 3422, 12, 610, 186, 84, 130, 2211, 68, 138, 2485, 18, 292, 555, 8, 1463, 78, 632, 60, 6806, 12
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7*3*5=105.
a(9)=2*4*17=136.
a(10)=2*3*2=12.
a(11)=19*2*2=76.
a(12)=5*3*7=105.
a(13)=2*11*23=506,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

a(43) corrected by R. J. Mathar, Apr 14 2010

A143852 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (abs(1-2-3-2, 2-5-2-3, 7-2-3-3, 2-2-5-11, 2-2-3-13, 2-7-3-5,..)).

Original entry on oeis.org

6, 8, 1, 16, 16, 13, 21, 20, 13, 34, 7, 17, 36, 37, 17, 27, 5, 13, 3, 29, 28, 6, 30, 8, 17, 66, 9, 1, 47, 52, 89, 8, 14, 77, 41, 81, 6, 31, 1, 1, 91, 8, 124, 13, 31, 13, 82, 17, 55, 69, 103, 10, 13, 100, 119, 18, 155, 6, 91, 40, 111, 11, 32, 55, 9, 10, 15, 37, 10, 115, 23, 124, 17
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 17 2008

Keywords

Examples

			Abs (2-7-3-5)=abs (-13) =13=a(6).
Abs (2-4-17-2)=abs(-21)=21=a(7).
Abs (3-2-19-2)=abs (-20)=20=a(8).
Abs (2-5-3-7)=abs (-13)=13=a(9).
Abs (2-11-23-2)=abs(-34)=34=a(10),
etc.

Links

Crossrefs

Cf. A141287, A141261, A136678, A143717.

Programs

  • Maple
    g:= proc(n) local F;
   F:= sort(ifactors(n)[2], (a,b) -> a[1]Robert Israel, Apr 25 2016
  • Mathematica
    Abs@ Total@ MapAt[Abs, Minus@ #, {1}] & /@ Partition[#, 4] &@ Flatten[FactorInteger /@ Range@ 134 /. {a_, b_} /; b == 1 :> {a}] (* Michael De Vlieger, Apr 25 2016 *)

Extensions

Corrected (10 replaced by 8) and extended by R. J. Mathar, Apr 18 2010

A143705 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes ((1+2)^3, (2+2)^5, (2+3)^7, (2+3)^3, (2+2)^5, (11+2)^2, (3+13)^2, (7+3)^5,..).

Original entry on oeis.org

27, 1024, 78125, 125, 1024, 169, 256, 100000, 16926659444736, 25, 441, 2097152, 41753905413413116367045797, 125, 49, 4096, 16384, 29791, 1296, 8589934592, 2476099, 81, 72759576141834259033203125, 9261, 3375
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=(7+3)^5=10^5=100000.
a(9)=(2+4)^17=6^17=16926659444736..
a(10)=(2+3)^2=5^2=25.
a(11)=(19+2)^2=21^2=441.
a(12)=(5+3)^7=8^7=2097152,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

Corrected (161051 removed) and extended by R. J. Mathar, Apr 18 2010
Showing 1-10 of 17 results. Next

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