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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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

A143706 (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

5, 9, 13, 9, 9, 24, 41, 26, 25, 8, 40, 22, 45, 9, 12, 42, 11, 61, 157, 26, 39, 16, 43, 41, 29, 207, 64, 15, 11, 93, 11, 16, 13, 36, 691, 14, 25, 40, 117, 7, 307, 95, 20, 67, 100, 21, 71, 106, 9, 148, 116, 6, 144, 19, 162, 19, 165, 7, 52, 89, 61, 981, 11, 93, 49, 109, 97, 112
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7*3+5=21+5=26.
a(9)=2*4+17=8+17=25.
a(10)=2*3+2=6+2=8.
a(11)=19*2+2=38+2=40.
a(12)=5*3+7=15+7=22.
a(13)=2*11+23=22+23=45,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

Corrected (9 duplicated, 75 replaced by 20 etc.) by R. J. Mathar, Apr 18 2010

A143707 (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

5, 14, 20, 12, 14, 44, 45, 56, 42, 10, 76, 50, 68, 12, 20, 78, 18, 145, 165, 70, 44, 28, 117, 44, 65, 215, 150, 26, 21, 140, 14, 28, 25, 68, 715, 24, 55, 154, 176, 10, 315, 155, 56, 75, 234, 38, 75, 390, 12, 150, 296, 8, 342, 32, 474, 35, 248, 10, 154, 92, 145, 1001, 21, 105
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7*(3+5)=7*8=56.
a(9)=2*(4+17)=2*21=42.
a(10)=2*(3+2)=2*5=10.
a(11)=19*(2+2)=19*4=40.
a(12)=5*(3+7)=5*10=50.
a(13)=2*(11+23)=2*34=68,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

Corrected (40 replaced by 76, 18 by 12, 90 by 70 etc.) by R. J. Mathar, Apr 18 2010

A143708 (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

1, 128, 1024, 64, 128, 14641, 14348907, 5764801, 2097152, 32, 130321, 9765625, 17179869184, 64, 625, 4826809, 512, 20511149, 116415321826934814453125, 6103515625, 4194304, 2401, 4052555153018976267, 4194304, 371293
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7^(3+5)=7^8=5764801.
a(9)=2^(4+17)=2^21=2097152.
a(10)=2^(3+2)=2^5=32.
a(11)=19^(2+2)=19^4=130321.
a(12)=5^(3+7)=5^10=9765625.
a(13)=2^(11+23)=2^34=17179869184,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

More terms from R. J. Mathar, Apr 18 2010

A143709 (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

4, 9, 15, 11, 9, 123, 1594325, 348, 33, 10, 363, 132, 2071, 11, 27, 2200, 11, 844, 4656612873077392578127, 136, 131077, 51, 46, 524291, 172, 45474735088646411895751953127, 2230, 15, 14, 8388655, 19, 51, 28, 291
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 13 2008

Keywords

Examples

			a(8)=7^3+5=343+5=348.
a(9)=2^4+17=16+17=43.
a(10)=2^3+2=8+2=10.
a(11)=19^2+2=361+2=363.
a(12)=5^3+7=125+7=132.
a(13)=2^11+23=2048+23=2071,
etc.

Crossrefs

Cf. A141287, A141261, A136735.

Extensions

Corrected (15 replaced by 9, 43 by 33) and extended by R. J. Mathar, Apr 18 2010

A144022 (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

0, 4, 5, 6, 10, 7, 13, 18, 7, 12, 3, 11, 22, 27, 11, 17, 1, 51, 9, 35, 32, 4, 26, 4, 11, 40, 3, 5, 43, 56, 85, 6, 12, 57, 35, 67, 0, 105, 3, 21, 67, 2, 42, 1, 55, 19, 88, 9, 49, 59, 97, 6, 9, 102, 87, 12, 49, 0, 101, 36, 107, 35, 26, 63, 15, 6, 97, 27, 6, 129, 33, 128, 21, 62, 121
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 17 2008

Keywords

Examples

			Abs (2-7+3-5)=abs (-7) =7=a(6).
Abs (2-4+17-2)=abs(13)=13=a(7).
Abs (3-2+19-2)=abs (18)=18=a(8).
Abs (2-5+3-7)=abs (-7)=7=a(9).
Abs (2-11+23-2)=abs(12)=12=a(10),
etc.

Crossrefs

Cf. A141287, A141261, A136678, A143717.

Extensions

Corrected (11 replaced by 9, 5 replaced by 6, 104 by 102) by R. J. Mathar, Apr 18 2010

A144076 (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

7, 11, 2, 19, 17, 24, 68, 37, 20, 253, 14, 40, 41, 44, 24, 90, 6, 4, 2, 28, 28, 9, 75, 13, 18, 77, 12, 2, 64, 52, 148, 13, 61, 736, 72, 104, 9, 4, 1, 60, 1026, 15, 3403, 24, 72, 12, 81, 88, 98, 252, 110, 15, 22, 199, 1750, 41, 206, 7, 88, 75, 222, 98, 87, 112, 8, 19, 64, 156
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 17 2008

Keywords

Examples

			Abs (2-7*3-5)=abs (-24) =24=a(6).
Abs (2-4*17-2)=abs(-68)=68=a(7).
Abs (3-2*19-2)=abs (-37)=37=a(8).
Abs (2-5*3-7)=abs (-20)=20=a(9).
Abs (2-11*23-2)=abs(-253)=253=a(10),
etc.

Crossrefs

Cf. A141287, A141261, A136678, A143717.

Extensions

Corrected (12 replaced by 52) by R. J. Mathar, Apr 18 2010
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