login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A250201 Least b such that Phi_n(b, b-1) is prime. 2
2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 6, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 4, 5, 40, 2, 3, 2, 7, 2, 5, 3, 3, 2, 13, 3, 2, 14, 4, 22, 3, 3, 13, 2, 34, 5, 3, 5, 2, 2, 34, 9, 2, 17, 7, 3, 2, 3, 18, 9, 47, 4, 20, 3, 2, 2, 8, 2, 4, 17, 6, 14, 2, 2, 61, 18, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Phi_n(b, b-1) = (b-1)^EulerPhi(n) * Phi_n(b/(b-1)).

This sequence is not defined at n = 1 since Phi_1(b, b-1) = 1 for all b, and 1 is not prime. Conjecture: a(n) is defined for all n>1.

If b = 1, then Phi_n(b, b-1) = 1 for all n, and 1 is not prime, so all a(n) > 1.

a(n) = 2 if and only if n is in A072226.

n        Phi_n(a, b)

1        a-b

2        a+b

3        a^2+ab+b^2

4        a^2+b^2

5        a^4+a^3*b+a^2*b^2+a*b^3+b^4

6        a^2-ab+b^2

...      ...

n        b^EulerPhi(n)*Phi_n(a/b)

LINKS

Eric Chen, Table of n, a(n) for n = 2..490

EXAMPLE

a(11) = 6 because Phi_11(b, b-1) is composite for b = 2, 3, 4, 5 and prime for b = 6.

a(37) = 40 because Phi_37(b, b-1) is composite for b = 2, 3, 4, ..., 39 and prime for b = 40.

MATHEMATICA

Table[k = 2; While[!PrimeQ[(k-1)^EulerPhi(n)*Cyclotomic[n, k/(k-1)]], k++]; k, {n, 2, 300}]

PROG

a(n) = for(k = 2, 2^16, if(ispseudoprime((k-1)^eulerphi(n) * polcyclo(n, k/(k-1))), return(k)))

CROSSREFS

Cf. A103794, A253633, A085398, A058013.

Sequence in context: A058515 A126696 A244464 * A252375 A339170 A257773

Adjacent sequences:  A250198 A250199 A250200 * A250202 A250203 A250204

KEYWORD

nonn

AUTHOR

Eric Chen, Mar 09 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 09:09 EST 2020. Contains 338702 sequences. (Running on oeis4.)