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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A102018 Numbers n>1 with the property that the decimal expansion of n is a permutation of the digits of the decimal expansion of phi(n) and the ratio n/phi(n) is a new record low value.

Original entry on oeis.org

21, 291, 2817, 2991, 4435, 20617, 45421, 69271, 75841, 162619, 176569, 284029, 400399, 474883, 732031, 778669, 783169, 1014109, 1288663, 1504051, 1514419, 1924891, 1956103, 2006737, 2044501, 2094901, 2239261, 2710627, 2868469, 3582907, 3689251, 4198273, 4696009
Offset: 1

Views

Author

Gunnar Arn Stefainsson (gos(AT)hell.is), Jun 19 2007

Keywords

Comments

Subsequence of A115921. - Michel Marcus, Jul 10 2015

Links

Crossrefs

Cf. A000010, A115921.

Programs

  • PARI
    lista(nn) = {mre = 2; for (n=2, nn, en = eulerphi(n); if (vecsort(digits(n)) == vecsort(digits(en)), re = n/en; if (re < mre, print1(n, ", "); mre = re);););} \\ Michel Marcus, Jul 10 2015

Extensions

More terms from Michel Marcus, Jul 10 2015
Removed initial 1 and changed definition, following discussion in Sequence Fans Mailing List by Michel Marcus and others. - N. J. A. Sloane, Jul 15 2015

A216385 Number of values of k for which phi(k) is a permutation of decimal digits of k, for k < 10^n.

Original entry on oeis.org

1, 3, 5, 21, 78, 403, 2069, 11856, 70835, 437164
Offset: 1

Views

Author

V. Raman, Sep 06 2012

Keywords

Examples

			a(3) = 5 because the values of k satisfying the condition for k < 10^3 are {1, 21, 63, 291, 502}. - _V. Raman_, Feb 17 2014

Crossrefs

Cf. A115921, A000010.

Programs

  • PARI
    a(n)=sum(k=1, 10^n, vecsort(digits(k)) == vecsort(digits(eulerphi(k)))) \\ Use digits(n)=eval(Vec(Str(n))) in old versions of PARI. - V. Raman, Feb 17 2014, based on edits by M. F. Hasler

Formula

a(n) = # { k in A115921 | k < 10^n }. - M. F. Hasler, Feb 24 2014

Extensions

a(9) from Jinyuan Wang, Mar 03 2020
a(10) from Amiram Eldar, Nov 30 2024

A216387 Number of values of k for which phi(k) is a permutation of decimal digits of k, for 10^(n-1) < k < 10^n.

Original entry on oeis.org

1, 2, 2, 16, 57, 325, 1666, 9787, 58979, 366329
Offset: 1

Views

Author

V. Raman, Sep 06 2012

Keywords

Examples

			a(3) = 2 because the values of k satisfying the condition for 10^2 < k < 10^3 are {291, 502}. - _V. Raman_, Feb 17 2014

Crossrefs

Cf. A000010 (phi), A115921.

Programs

  • PARI
    a(n)=sum(k=10^(n-1), 10^n, vecsort(digits(k)) == vecsort(digits(eulerphi(k)))) \\ V. Raman, Feb 17 2014, based on edits by M. F. Hasler

Formula

a(n) = # { k in A115921 | 10^(n-1) < k < 10^n }. - M. F. Hasler, Feb 24 2014

Extensions

a(9)-a(10) from Amiram Eldar, May 19 2024
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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