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.

A230004 Numbers n such that phi(n) + sigma(n) = reversal(n) + 4.

Original entry on oeis.org

499, 2836, 4999, 49999, 280036, 4999999, 28000036, 283682836, 2800000000036
Offset: 1

Views

Author

Farideh Firoozbakht, Nov 07 2013

Keywords

Comments

If p=5*10^m-1 is prime (m is a term of A056712) then p is in the sequence.
Let p(m,n) = 10^(m+3)*(7*10^(m+2)+92)*(10^((m+4)*n)-1)/(10^(m+4)-1) +7*10^(m+1)+9, if m>0, n>=0 and p(m,n) is prime then 4*p(m,n) is in the sequence.
All known terms are of these two forms.
What is the smallest term of the sequence which is not of the form p or 4*p where p is prime?
Note that a(2)=4*p(1,0), a(5)=4*p(3,0), a(7)=4*p(5,0) and a(8)=4*p(1,1).

Examples

			phi(499)+sigma(499) = 498+500 = 994+4 = reversal(499)+4, so 499 is in the sequence.

Crossrefs

Cf. A000010, A000203, A004086, A056712, A230005.

Programs

  • Mathematica
    r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[1,n] + EulerPhi[n] == r[n] + 4, Print[n]], {n,1050000000}]
Select[Range[5*10^6],EulerPhi[#]+DivisorSigma[1,#]==IntegerReverse[#]+4&] (* The program generates the first 6 terms of the sequence. *) (* Harvey P. Dale, Dec 28 2024 *)
  • PARI
    is(n)=subst(Polrev(digits(n)),'x,10)+4==eulerphi(n)+sigma(n) \\ Charles R Greathouse IV, Nov 08 2013

Extensions

a(9) from Giovanni Resta, Feb 06 2014

A230006 Numbers k such that sigma(k) + phi(k) = reversal(k) + 1.

Original entry on oeis.org

1, 37, 225, 397, 11112722, 1309286244182
Offset: 1

Views

Author

Farideh Firoozbakht, Dec 02 2013

Keywords

Comments

If p = 4*10^m-3 is prime then p is in the sequence.
a(7) > 10^13. - Giovanni Resta, Feb 08 2014

Examples

			sigma(37)+phi(37) = 38+36 = 73+1 = reversal(37)+1.

Crossrefs

Cf. A000010, A000203, A004086, A101398, A230004, A230005.

Programs

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

Extensions

a(6) 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.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.