A141270 -id:A141270 - cp's OEIS frontend

A136738 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13,..) transform in (01+2, 32+2, 52+3, 72+3, 32+2, 511+2, 23+13,..).

2, 8, 13, 17, 8, 57, 19, 17, 14, 37, 40, 13, 25, 49, 17, 29, 8, 205, 46, 13, 39, 37, 8, 93, 41, 56, 13, 88, 35, 33, 98, 23, 12, 53, 79, 9, 57, 24, 67, 120, 76, 65, 16, 43, 17, 136, 74, 17, 145, 79, 77, 12, 45, 25, 1029, 23, 49, 168, 26, 77, 89, 122, 8, 48, 27, 95, 254, 13, 201, 8

Offset: 1

Juri-Stepan Gerasimov, Oct 31 2008

nonn

			0*1+2=2=a(1).
3*2+2=8=a(2).
5*2+3=13=a(3).
7*2+3 =17=a(4).
3*2+2=8=a(5).
5*11+2=57=a(6).
2*3+13 =19=a(7).
2*7+3=19=a(8), etc.

Cf. A141269, A141270.

a(8), a(16), a(19) etc. corrected by R. J. Mathar, Apr 25 2010

A143651 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13, ...) becomes (0^1 + 2, 3^2 + 2, 5^2 + 3, 7^2 + 3, 3^2 + 2, 5^11 + 2, 2^3 + 13, ...).

Original entry on oeis.org

2, 11, 28, 52, 11, 48828127, 21, 131, 29, 292, 524290, 35, 60, 532, 245, 8195, 11, 3219905755813179726837609, 274, 35, 138, 78127, 10, 1388, 1594325, 284, 15, 1851, 1333, 48, 2213, 2189, 34, 129140165, 8245, 11, 48828127, 2190, 390, 3483, 304

Offset: 1

Juri-Stepan Gerasimov, Nov 01 2008

nonn

			0^1 + 2 = 0 + 2 = 2 = a(1).
3^2 + 2 = 9 + 2 = 11 = a(2).
5^2 + 3 = 25 + 3 = 28 = a(3).
7^2 + 3 = 49 + 3 = 52 = a(4).
3^2 + 2 = 9 + 2 = 11 = a(5).
5^11 + 2 = 48828125 + 2 = 48828127 = a(6).
2^3 + 13 = 8 + 13 = 21 = a(7).
2^7 + 3 = 128 + 3 = 131 = a(8), etc.

Cf. A141269, A141270.

pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [0,1] ; 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(120) : for n from 1 to nops(pL)-4 by 3 do printf("%d,", op(n, pL)^op(n+1, pL)+op(n+2,pL) ) ; od: # R. J. Mathar, Nov 06 2008

a(11) corrected, extended by R. J. Mathar, Nov 06 2008

A143675 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (0^(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

0, 81, 390625, 5764801, 81, 3761581922631320025499956919111186169019729781670680068828005460090935230255126953125

Offset: 1

Juri-Stepan Gerasimov, Nov 01 2008

nonn

			0^(1^2)=0^1=0=a(1).
3^(2^2)=3^4=81=a(2).
5^(2^3)=5^8=390625=a(3).
7^(2^3)=7^8=5764801=a(4).
3^(2^2)=3^4=81=a(5), etc.

Cf. A141269, A141270.

One more term from R. J. Mathar, Apr 18 2010

A143676 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (abs (0-1-2, 3-2-2, 5-2-3, 7-2-3, 3-2-2, 5-11-2, 2-3-13,..)).

Original entry on oeis.org

3, 1, 0, 2, 1, 8, 14, 8, 1, 12, 19, 6, 6, 18, 4, 14, 1, 24, 33, 6, 8, 4, 3, 16, 12, 43, 8, 39, 6, 20, 41, 6, 5, 16, 64, 4, 8, 7, 12, 55, 63, 32, 7, 12, 12, 63, 9, 10, 66, 72, 38, 1, 24, 6, 68, 4, 39, 79, 9, 28, 28, 97, 3, 15, 23, 30, 23, 6, 88, 3, 7, 98, 18, 98, 5, 48, 103, 109, 14, 36, 116, 20

Offset: 1

Juri-Stepan Gerasimov, Nov 01 2008

nonn

			Abs(0-1-2)=abs(-3)=3=a(1).
Abs(3-2-2)=abs(-1)=1=a(2).
Abs(5-2-3)=abs(0)=0=a(3).
Abs(7-2-3)=abs(2)=2=a(4).
Abs(3-2-2)=abs(-1)=1=a(5).
Abs(5-11-2)=abs(-8)=8 =a(6).
Abs(2-3-13)=abs(-14)=14=a(7), etc.

Cf. A141269, A141270.

pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [0,1] ; 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

Abs[#[[1]]-#[[2]]-#[[3]]]&/@Partition[Join[{0,1},Flatten[Table[ DeleteCases[ Flatten[FactorInteger[n]],1],{n,2,120}]]],3] (* Harvey P. Dale, Apr 02 2015 *)

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

cp's OEIS Frontend

A136738 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13,..) transform in (01+2, 32+2, 52+3, 72+3, 32+2, 511+2, 23+13,..).

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A143651 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13, ...) becomes (0^1 + 2, 3^2 + 2, 5^2 + 3, 7^2 + 3, 3^2 + 2, 5^11 + 2, 2^3 + 13, ...).

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A143675 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (0^(1^2), 3^(2^2), 5^(2^3), 7^(2^3), 3^(2^2), 5^(11^2), 2^(3^13),..).

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Author

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Examples

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Extensions

A143676 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (abs (0-1-2, 3-2-2, 5-2-3, 7-2-3, 3-2-2, 5-11-2, 2-3-13,..)).

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Examples

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Mathematica

Extensions

cp's OEIS Frontend

A136738 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) transform in (0*1+2, 3*2+2, 5*2+3, 7*2+3, 3*2+2, 5*11+2, 2*3+13,..).

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Author

Keywords

Examples

Crossrefs

Extensions

A143651 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, ...) becomes (0^1 + 2, 3^2 + 2, 5^2 + 3, 7^2 + 3, 3^2 + 2, 5^11 + 2, 2^3 + 13, ...).

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Extensions

A143675 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (0^(1^2), 3^(2^2), 5^(2^3), 7^(2^3), 3^(2^2), 5^(11^2), 2^(3^13),..).

Views

Author

Keywords

Examples

Crossrefs

Extensions

A143676 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (abs (0-1-2, 3-2-2, 5-2-3, 7-2-3, 3-2-2, 5-11-2, 2-3-13,..)).

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

Extensions

A136738 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^23, 13,..) transform in (01+2, 32+2, 52+3, 72+3, 32+2, 511+2, 23+13,..).

A143651 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13, ...) becomes (0^1 + 2, 3^2 + 2, 5^2 + 3, 7^2 + 3, 3^2 + 2, 5^11 + 2, 2^3 + 13, ...).

A143675 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (0^(1^2), 3^(2^2), 5^(2^3), 7^(2^3), 3^(2^2), 5^(11^2), 2^(3^13),..).

A143676 (0, 1, 2, 3, 2^2, 5, 23, 7, 2^3, 3^2, 25, 11, 2^2*3, 13,..) becomes (abs (0-1-2, 3-2-2, 5-2-3, 7-2-3, 3-2-2, 5-11-2, 2-3-13,..)).