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 1-6 of 6 results.

A114928 Numbers n such that sigma(n)=4*reversal(n).

Original entry on oeis.org

42, 402, 492, 4000002, 57906504, 400000002, 4000000002, 6279090751, 62698513951, 400000000002
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 28 2006

Keywords

Comments

If p=(2*10^n+1)/3 is prime then m=6*p is in the sequence because sigma(m)=sigma(6*p)=12*(2*10^n+4)/3=4*(2*10^n+4)=4* reversal(4*10^n+2)=4*reversal(6*(2*10^n+1)/3)=4*reversal(6*p) =4*reversal(m). Next term is greater than 5*10^8.
a(11) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			492 is in the sequence because sigma(492)=sigma(4*3*41)=7*4*42
=4*294=4*reversal(492).

Crossrefs

Cf. A069216, A105324, A114927.

Programs

  • Mathematica
    Do[If[DivisorSigma[1, n]==4*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 500000000}]

Extensions

a(7)-a(9) from Donovan Johnson, Dec 21 2008
a(10) from Giovanni Resta, Oct 28 2012

A114927 Numbers n such that sigma(n)=3*reversal(n).

Original entry on oeis.org

41, 291552, 692133, 2946762, 8231796, 21732508611, 27892659612
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 28 2006

Keywords

Comments

No more terms through 10^9. - Ryan Propper, Jan 08 2007
a(8) > 10^12. - Giovanni Resta, Oct 28 2012

Crossrefs

Cf. A069216, A105324, A114928.

Programs

  • Mathematica
    Do[If[DivisorSigma[1, n] == 3*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 20000000}]

Extensions

a(6)-a(7) from Donovan Johnson, Dec 21 2008

A249899 Numbers k such that sigma(k) contains the same digits as k in base 10.

Original entry on oeis.org

1, 69, 211, 258, 270, 276, 433, 609, 639, 787, 877, 1021, 1201, 1231, 1255, 1291, 1321, 1433, 1621, 1721, 1787, 1877, 2011, 2111, 2131, 2141, 2161, 2204, 2311, 2391, 2411, 2556, 2676, 2711, 2931, 3121, 3343, 3409, 3413, 3433, 3463, 3554, 3643, 3678, 3679, 3877
Offset: 1

Views

Author

Jaroslav Krizek, Jan 05 2015

Keywords

Comments

Supersequence of A115920 and A069216.

Examples

			211 is in the sequence because the set of digits of n {1, 2} equals the set of digits of sigma(211) = 212.

Links

Crossrefs

Cf. A000203, A069216, A115920.

Programs

  • Magma
    [n: n in [1..10^5] | Set(Intseq(n)) eq Set(Intseq(SumOfDivisors(n)))];
  • Mathematica
    Select[Range[4000],Union[IntegerDigits[DivisorSigma[1,#]]] == Union[ IntegerDigits[#]]&] (* Harvey P. Dale, Dec 29 2015 *)
  • PARI
    isok(n) = Set(digits(n)) == Set(digits(sigma(n))); \\ Michel Marcus, May 27 2018

A115748 Numbers n such that sigma(n)=7*reversal(n).

Original entry on oeis.org

63301, 651001, 6967932, 2158803990, 88858402692
Offset: 1

Views

Author

Farideh Firoozbakht, Feb 12 2006

Keywords

Comments

a(6) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			2158803990 is in the sequence because sigma(2158803990)
=6951619584=7*993088512=7*reversal(2158803990).

Crossrefs

Cf. A069216, A105324, A114928.

Extensions

a(5) from Donovan Johnson, Dec 21 2008

A115749 Numbers n such that sigma(n)=8*reversal(n).

Original entry on oeis.org

861, 951, 2070, 8241, 900051, 8864151, 9000051, 82000041, 8200000041, 82000000041
Offset: 1

Views

Author

Farideh Firoozbakht, Feb 12 2006

Keywords

Comments

If p=3*10^n+17 is prime then 3*p is in the sequence because sigma(3*p)=4*(3*10^n+18)=12*10^n+72=8*(15*10^(n-1)+9)=8* reversal(9*10^n+51)=8*reversal(3*p). Also if p=(2*10^n+1)/3 is prime then 123*p is in the sequence (the proof is easy). Next term is greater than 13*10^7.
a(11) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			82000041 is in the sequence because sigma(82000041)
=112000224=8*14000028=8*reversal(82000041).

Crossrefs

Cf. A069216, A105324, A114928, A115747, A115748.

Programs

  • Mathematica
    Do[If[DivisorSigma[1,n]==8*FromDigits[Reverse[IntegerDigits[n]]],Print[n]],{n,130000000}]

Extensions

a(9)-a(10) from Donovan Johnson, Dec 21 2008

A136542 Numbers n such that sigma(n)=reversal(n)+5.

Original entry on oeis.org

57, 58, 597, 1642, 5997, 5998, 51718, 160042, 556438, 599997, 5999998, 15810772, 59999997, 59999998, 160000000042
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 08 2008

Keywords

Comments

I. If 2*10^m-1 is prime then n=3*(2*10^m-1) is in the sequence(the proof is easy).
II. If 3*10^m-1 is prime then n=2*(3*10^m-1) is in the sequence (the proof is easy).
III. If m>1 and 8*10^m+21 is prime then n=2*(8*10^m+21) is in the sequence(the proof is easy).
a(16) > 10^12. - Giovanni Resta, Oct 28 2012

Examples

			sigma(57)=80=75+5=reversal(57)+5, so 57 is in the sequence.

Crossrefs

Cf. A069216.

Programs

  • Mathematica
    Do[If[DivisorSigma[1,n]==FromDigits@Reverse@IntegerDigits#n+5, Print[n]],{n,160000000}]

Extensions

a(15) from Giovanni Resta, Oct 28 2012
Showing 1-6 of 6 results.

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