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.

A230005 Numbers n such that phi(n) + sigma(n) = reversal(n) - 4.

Original entry on oeis.org

489, 4629, 296206, 460029, 29589106, 46000029, 2927272726, 4045046518, 21223345084, 29600331295, 296151515206, 460000000029
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 07 2013

Keywords

Comments

If p = 15*10^k+10+(10^k-1)/3 is prime then 3*p is in the sequence.
a(7) is greater than 1.3*10^8.
a(11) > 10^11. - Donovan Johnson, Nov 08 2013
If p=(1/11)*(23*100^m-1) is prime then 14*p is a term of the sequence. - Farideh Firoozbakht, Nov 08 2013
a(13) > 10^13. - Giovanni Resta, Feb 08 2014
If p = (1685*10^(2k+2)+31)/33 is prime then 58*p is in the sequence. For k = 0, 3, 9, 30, 42, 51, 120, 846, ... p is prime. - Farideh Firoozbakht, Feb 10 2014

Examples

			489 is in the sequence because phi(489)+sigma(489) = 324+656 = 984-4 = reversal(489)-4.

Crossrefs

Cf. A000010, A000203, A004086, A070272, A230004, A230006, A230019, A136544, A237521, A237522.

Programs

  • Mathematica
    Do[If[FromDigits@Reverse@IntegerDigits@n-4 == EulerPhi[n] + DivisorSigma[1, n], Print[n]], {n, 130000000}]
  • PARI
    is(n)=subst(Polrev(digits(n)),'x,10)-4==eulerphi(n)+sigma(n) \\ Charles R Greathouse IV, Nov 08 2013

Extensions

a(7)-a(10) from Donovan Johnson, Nov 08 2013
a(11)-a(12) from Giovanni Resta, Feb 06 2014

A136544 Numbers n such that phi(n)+sigma(n)=reversal(n)+3.

Original entry on oeis.org

3, 3997, 3999997, 168632373, 399999999997, 3999999999997
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 20 2008

Keywords

Comments

Next term of the sequence is greater than 10^9. All semiprimes of the form 4*10^m-3 are in the sequence - the proof is easy. For m=3,6,11,12,13,15,16,18,19,24,38,56,60,... 4*10^m-3 is semiprime. Is it true that 3 is the only prime term in the sequence?
a(7) > 10^13. - Giovanni Resta, Feb 08 2014

Examples

			phi(168632373)+sigma(168632373)=87744384+285492480=373236861+3= reversal(168632373)+3, so 168632373 is in the sequence.

Crossrefs

Cf. A070272, A230004, A230005, A230006, A230019, A237521, A237522.

Programs

  • Mathematica
    Do[If[DivisorSigma[1,n]+EulerPhi@n==FromDigits@Reverse@IntegerDigits@n+ 3,Print[n]],{n,500000000}]

Extensions

a(5) from Giovanni Resta, Nov 03 2012
a(6) from Giovanni Resta, Feb 06 2014

A230019 Numbers n such that sigma(n) + phi(n) = reversal(n) - 3.

Original entry on oeis.org

199993, 17333334, 19999993, 199999999993, 1999999999993
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 02 2013

Keywords

Comments

If n=2*10^m-7 is a semiprime then n is in the sequence. Also if p=(1/999)*(962*1000^m+37) is prime then 18*p is in the sequence. All known terms are of these two forms.
a(6) > 10^13. - Giovanni Resta, Feb 08 2014

Crossrefs

Cf. A000010, A000203, A004086, A070272, A230004, A230005, A230006, A136544, A237521, A237522.

Programs

  • Mathematica
    r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[1, n] + EulerPhi[n] == r[n]-3, Print[n]], {n, 1000000000}]

Extensions

a(4)-a(5) from Giovanni Resta, Feb 06 2014

A237521 Numbers k such that phi(k) + sigma(k) = reversal(k) + 2.

Original entry on oeis.org

2, 22605, 26026, 492775589
Offset: 1

Views

Author

Giovanni Resta, Feb 08 2014

Keywords

Comments

a(5), if it exists, is larger than 10^13.
Up to 10^13 the equation phi(k) + sigma(k) = reversal(k) - 2 is satisfied only by k = 26330276.

Examples

			22605 is in the sequence because phi(22605) = 10880, sigma(22605) = 39744, and 10880 + 39744 = 50622 + 2, where 50622 is the reversal of 22605.

Crossrefs

Cf. A000010, A000203, A004086.
Cf. A070272, A230004, A230005, A230006, A230019, A136544, A237522.

Programs

  • Mathematica
    Select[Range[493*10^6],EulerPhi[#]+DivisorSigma[1,#]== IntegerReverse[ #]+2&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 01 2020 *)

A237522 Numbers k such that phi(k) + sigma(k) = reversal(k) - 1.

Original entry on oeis.org

25, 165261124, 1698757933
Offset: 1

Views

Author

Giovanni Resta, Feb 08 2014

Keywords

Comments

a(4), if it exists, is larger than 10^13.

Examples

			k = 165261124 is a term, because phi(k) = 67233600, sigma(k) = 353928960 and 67233600 + 353928960 = 421162561 - 1, where 421162561 is the reversal of 165261124.

Crossrefs

Cf. A000010, A000203, A004086.
Cf. A070272, A230004, A230005, A230006, A230019, A136544, A237521.

A178323 Numbers n such that phi(reversal(n)) + sigma(reversal(n)) = n.

Original entry on oeis.org

572, 592, 5992, 599992, 2014080, 5999992, 594637872, 599999992, 599999999992
Offset: 1

Views

Author

Farideh Firoozbakht, May 28 2010

Keywords

Comments

If n is in the sequence A070272 then reversal(n) is in this sequence. 10 divides all other terms of the sequence. 2014080 is the only known such term.
If p=6*10^n-1 is a prime greater than 5 then reversal(5*p) is in the sequence, see comment lines of A070272.
There is no further term up to 10^9.
10^12 < a(10) <= 1442827967760. - Giovanni Resta, Sep 04 2018

Examples

			2014080 = phi(804102) + sigma(804102), so 2014080 is in the sequence.

Crossrefs

Cf. A000010, A000203, A004086, A070272, A178324, A178325.

Programs

  • Mathematica
    r[n_]:=FromDigits[Reverse[IntegerDigits[n]]];
Do[If[EulerPhi[r[n]]+DivisorSigma[1,r[n]]==n,Print[n]],{n,1000000000}]

Extensions

a(9) from Giovanni Resta, Sep 04 2018
Showing 1-6 of 6 results.

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