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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A114930 Numbers n such that phi(n)=2*reversal(n).

Original entry on oeis.org

6180, 27630, 2914830, 4471740, 27000630, 637062480, 27000000630, 679410757980, 4412687534631, 4421625783741
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 29 2006

Keywords

Comments

If m>1 and p=3*10^m+7 is prime then 90*p is in the sequence because phi(90*p)=phi(90)*phi(p)=24*(3*10^m+6)=2*(36*10^m+72) =2*reversal(27*10^m+63)=2*reversal(9*p)=2*reversal(90*p). Note that 30 divides all known terms of this sequence. Next term is greater than 11*10^7.
a(11) > 10^13. - Giovanni Resta, Aug 12 2019

Examples

			637062480 is a term because phi(637062480) = 2*84260736 = 2*reversal(637062480).

Crossrefs

Cf. A000010, A004086, A069215, A114930, A136539, A114931, A136538.

Programs

  • Mathematica
    Do[If[EulerPhi[n]==2*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 110000000}]

Extensions

a(6)-a(8) from Giovanni Resta, Oct 28 2012
a(9)-a(10) from Giovanni Resta, Aug 12 2019

A114931 Numbers n such that phi(n)=4*reversal(n).

Original entry on oeis.org

10, 20, 40, 50, 80, 210, 420, 630, 711, 831, 840, 2910, 29910, 40320, 80640, 98361, 673140, 865580, 8656341, 466760130, 694602930, 821412711, 23465346510, 40396039620, 63130473930, 234000006510, 464205665820, 2340653406510, 2346599346510
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 29 2006

Keywords

Comments

If p=10^m-3 is prime then 30*p is in the sequence because phi(30*p)=phi(30)*phi(p)=8*(10^m-4)=4*(2*10^m-8)=4*reversal (3*10^m-9)=4*reversal(3*p)=4*reversal(30*p). Next term is greater than 55*10^7.
Let f(m,n)=(78*10^(m+3)+210)*(10^(n*(m+4))-1)/(10^(m+4)-1)+7, if p=f(m,n) is prime then 30*p is a term of the sequence. - Jahangeer Kholdi, Nov 13 2013
Also if p=(1/101)*(680*10000^n+27) is prime then 60*p is in the sequence. - Jahangeer Kholdi, Nov 13 2013
a(30) > 10^13. - Giovanni Resta, Aug 12 2019

Examples

			20 is in the sequence because phi(20)=4*2=4*reversal(20).

Crossrefs

Cf. A000010, A004086, A069215, A114930, A136538.

Programs

  • Mathematica
    Do[If[EulerPhi[n]==4*FromDigits[Reverse[IntegerDigits[n]]], Print[n]], {n, 550000000}]

Extensions

a(21)-a(27) from Giovanni Resta, Oct 28 2012
a(28)-a(29) from Giovanni Resta, Aug 12 2019
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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