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.

Previous Showing 11-13 of 13 results.

A136538 Numbers n such that reversal(n)=2*phi(n).

Original entry on oeis.org

2, 4, 8, 42, 84, 2763, 4032, 8064, 67314, 86558, 291483, 2700063, 2700000063, 4039603962, 46420566582, 6739054689866
Offset: 1

Views

Author

Farideh Firoozbakht, Jan 04 2008

Keywords

Comments

If m>1 and p=3*10^m+7 is prime then n=9*p is in the sequence (the proof is easy). If n is an even term of the sequence and the largest digit of n is less than 5(3) then 2n is (both numbers 2n & 4n are) in the sequence (the proof is easy).
a(17) > 10^13. - Giovanni Resta, Aug 12 2019

Examples

			Reversal(42)=24=2*12=2*phi(42), so 42 is in the sequence. [Example corrected Jan 25 2008]

Crossrefs

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

Programs

  • Mathematica
    Do[If[FromDigits@Reverse@IntegerDigits@n==2*EulerPhi[n], Print[n]],{n,100000000}]

Extensions

a(13)-a(15) from Giovanni Resta, Oct 28 2012
a(16) from Giovanni Resta, Aug 12 2019

A113622 Numbers k such that the reverse of the representation of phi(k) is a substring of k, in base 10.

Original entry on oeis.org

1, 21, 63, 270, 291, 1065, 2991, 6102, 10087, 10279, 10654, 16528, 144069, 1440069, 10253179, 10657654, 14400069, 16163608, 46676013, 69460293, 2346534651, 2369436474, 6313047393, 10270341004, 10657657654, 14406534069, 23400000651
Offset: 1

Views

Author

Giovanni Resta, Jan 26 2006

Keywords

Comments

If p = 480...023 is prime, then k = 3*p = 1440...069 and phi(k) = 960...044, thus k belongs to the sequence.

Examples

			phi(1_440069) = 960044.

Crossrefs

Cf. A000010, A069215.

Programs

  • Mathematica
    lst = {}; Do[If[{}!= StringPosition[ToString@n, StringReverse@ToString@EulerPhi@n], AppendTo[lst, n]], {n, 2*10^7}]; lst

Extensions

a(19)-a(27) from Donovan Johnson, May 11 2010

A097644 Numbers n such that pi(n) = reversal(n).

Original entry on oeis.org

51, 130, 370, 8201, 73270, 82080, 26113610, 4854248220, 37682961610
Offset: 1

Views

Author

Farideh Firoozbakht, Aug 25 2004

Keywords

Comments

This sequence has only two odd terms, i.e., 51 and 8201 and 10 divides all other terms. Next term is greater than 10^8.

Examples

			26113610 is in the sequence because
pi(26113610) = 1631162 = reversal(26113610).

Crossrefs

Cf. A037171, A069215.

Programs

  • Mathematica
    Do[If[PrimePi[m]==FromDigits[Reverse[IntegerDigits[m]]], Print[m]], {m, 100000000}]

Extensions

Two more terms from Giovanni Resta, Feb 06 2006
Previous Showing 11-13 of 13 results.

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

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