A063104 a(0) = 0, a(n) = smallest composite k such that phi(k + 2^n) = phi(k) + 2^n; also cototient(k + 2^n) = cototient(k).

0, 6, 12, 24, 39, 84, 69, 75, 213, 1092, 249, 1131, 8736, 13413, 21201, 1275, 2193, 279552, 98337, 968727, 71085, 2783555, 646869, 3145959, 1805781, 5798435, 787605, 27962075, 2073033, 282181709, 1150329, 10380353, 516201, 150807855, 141521295, 860867981

Offset: 0

Author

Labos Elemer, Aug 08 2001

Keywords

• nonn

Examples

			n=4, a(4)=39, Phi[39]+16=24+16=40=Phi[55]; a(14) = 21201, Phi(21201) + 2^14 = 13680 + 16384 = 30064 = Phi(37585).
		

Crossrefs

Cf. A000010, A051953, A055458, A063500, A054987.

Programs

Mathematica

Do[k = 4; While[ PrimeQ[k] || EulerPhi[k + 2^n] != EulerPhi[k] + 2^n, k++ ]; Print[k], {n, 1, 28} ]

PARI

{ n=0; f="b063104.txt"; write(f, "0 0"); for (n=1, 28, k=4; while (isprime(k) || eulerphi(k + 2^n) != eulerphi(k) + 2^n, k++); write(f, n, " ", k) ) } \\ Harry J. Smith, Aug 18 2009

Formula

a(n) = Min{x: A000010(n)+2^n = A000010(x+2^n)} = Min{x: A051953(x+2^n) = A051953(n)}

Extensions

More terms from Robert G. Wilson v, Nov 03 2001

a(29)-a(35) from Donovan Johnson, Aug 18 2011