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 1-3 of 3 results.

A066902 Integers k such that phi(prime(k)+1) = phi(prime(k)-1).

Original entry on oeis.org

3, 5, 20, 156, 254, 377, 593, 1800, 5903, 5981, 7925, 18669, 19240, 41274, 48296, 135700, 146866, 228028, 234303, 251216, 407377, 654288, 802222, 886223, 938654, 1063412, 1072766, 1212140, 1238668, 1515063, 1609346, 2080991, 2097725, 2363130, 2408674, 2916514
Offset: 1

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Author

Benoit Cloitre, Jan 26 2002

Keywords

Comments

Integers k such that A008331(k) = A008330(k).

Links

Crossrefs

Cf. A000010, A008864, A006093, A008330, A008331, A067890.

Programs

  • Mathematica
    Select[Range[1000000],EulerPhi[Prime[#]-1]==EulerPhi[Prime[#]+1]&] (* Harvey P. Dale, Feb 25 2012 *)
  • PARI
    isok(k) = my(p=prime(k)); eulerphi(p+1) == eulerphi(p-1); \\ Michel Marcus, Apr 06 2020

Formula

a(n) = primepi(A067890(n)). - Giovanni Resta, Apr 06 2020

Extensions

More terms from Harvey P. Dale, Feb 25 2012
More terms from Jinyuan Wang, Apr 05 2020

A303549 Lesser of twin primes p for which phi(p-1) = phi(p+1), where phi(n) is the Euler totient function (A000010).

Original entry on oeis.org

5, 11, 71, 2591, 208391, 16692551, 48502931, 92012201, 249206231, 419445251, 496978301, 1329067391, 1837151681, 2277479051, 2647600061, 4733566391, 6435087011, 10327948751, 14089345691, 14923624031, 22415286251, 27508270301, 39662281331, 59013882071, 70353395351
Offset: 1

Views

Author

Amiram Eldar, Apr 26 2018

Keywords

Comments

Intersection of A001359 and A067890 (or A066812).
The terms below 10^8 were taken from the paper by Garcia et al.

Examples

			p = 5 is the lesser of the twin primes (5, 7), and phi(5-1) = phi(5+1) = 2.

Links

Crossrefs

Cf. A000010, A001359, A006512, A008330, A066812, A067890, A067933, A286714, A286715.

Programs

  • Mathematica
    seq={}; Do[p = Prime[i]; If[PrimeQ[p+2] && EulerPhi[p-1] == EulerPhi[p+1], AppendTo[seq, p]], {i, 1, 1000000}]; seq
  • PARI
    isok(p) = isprime(p) && isprime(p+2) && (eulerphi(p-1) == eulerphi(p+1)); \\ Michel Marcus, Apr 26 2018

Extensions

a(12)-a(16) from Michel Marcus, Apr 26 2018
a(17)-a(25) from Giovanni Resta, Apr 26 2018

A380091 Primes p such that phi(p+1) = 2*phi(p-1) where phi = A000010.

Original entry on oeis.org

2, 3, 7, 31, 991, 1951, 2521, 7411, 23431, 26731, 37441, 92431, 131071, 396631, 489061, 532141, 830551, 2811691, 3319171, 3698941, 4247167, 5239411, 6829681, 8326711, 8997871, 12625831, 12889231, 14756743, 15891121, 16125721, 16446301, 21203071
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 11 2025

Keywords

Comments

Primes in A258454 - 1.

Crossrefs

Cf. A000010, A066812, A067890, A258454.

Programs

  • Magma
    [p: p in PrimesUpTo(15*10^6) | 2*EulerPhi(p-1) eq EulerPhi(p+1)];
  • Mathematica
    Select[Prime[Range[10^5]], EulerPhi[# + 1] == 2*EulerPhi[# - 1] &] (* Amiram Eldar, Jan 12 2025 *)
Showing 1-3 of 3 results.

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

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