A110196 Numbers m such that k = 2m is the least k such that phi(m+k) = 2*phi(k).

1, 13, 23, 97, 113, 131, 199, 227, 491, 859, 929

Offset: 1

Author

T. D. Noe, Jul 15 2005

Keywords

• nonn
• more

Comments

Note that all m > 1 are primes.

No other terms below 10^8. - Max Alekseyev, Nov 18 2024

Links

• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010, A050473 (least k such that phi(n+k) = 2*phi(k)).

Programs

Mathematica

Do[k=1; While[EulerPhi[n+k] != 2*EulerPhi[k], k++ ]; If[k==2n, Print[n]], {n, 5000}]

PARI

f(n) = apply(x -> x - n, select(x -> x > n, invphi(2*eulerphi(n)))); \\ using Max Alekseyev's invphi.gp
lista(nmax) = {my(v = vector(nmax), c = 0, k = 1, s); while(c < nmax, s = f(k); for(i = 1, #s, if(s[i] <= nmax && v[s[i]] == 0, c++; v[s[i]] = k)); k++); for(i = 1, #v, if(v[i] == 2*i, print1(i, ", ")));} \\ Amiram Eldar, Nov 05 2024