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A058887 Smallest prime p such that (2^n)*p is a nontotient number. 4
3, 7, 17, 19, 19, 19, 31, 31, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n=8,9,...,582, a(n) = 47. Note that A040076(47)=583.

For n=583,584,...,6392, a(n) = 383. Note that A040076(383)=6393.

Subsequent primes are 2897, 3061, 5297, and 7013 (cf. A057192 and A071628).

Starting with some large N, a(n)=p for all n >= N. This prime p will likely be the first prime SierpiƄski number, which is conjectured to be 271129.

In particular, a(n) <= 271129 for all n.

REFERENCES

David Harden, Posting to Sequence Fans Mailing List, Sep 19 2010

LINKS

Table of n, a(n) for n=0..65.

D. Bressoud, CNT.m Computational Number Theory Mathematica package.

FORMULA

Min{p|p is prime and card(invphi((2^n)*p))=0}.

EXAMPLE

For n=1, the initial segment of {2p} sequence is nops(invphi({2p}))={4, 4, 2, 0, 2, 0, 0, 0, 2, 2, ...}, where the position of the first 0 is 4, corresponding to p(4)=7, so a(1)=7.

For n=8 the same initial segment is: {11, 32, 23, 18, 24, 10, 11, 4, 9, 21, 2, 16, 9, 12, 0, 14, 5, 6, 12, ...}, where the first 0 is the 15th, corresponding to p(15)=47, thus a(8)=47.

MATHEMATICA

Needs["CNT`"]; Table[p=3; While[PhiInverse[p*2^n] != {}, p=NextPrime[p]]; p, {n, 0, 20}]

PROG

(PARI) a(n) = my(p=2); while(istotient(2^n*p), p=nextprime(p+1)); p; \\ Michel Marcus, May 14 2020

CROSSREFS

Cf. A005277, A007617, A002020, A000010, A051953.

Sequence in context: A191147 A227211 A271725 * A306355 A087749 A140863

Adjacent sequences:  A058884 A058885 A058886 * A058888 A058889 A058890

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 08 2001

EXTENSIONS

Edited by T. D. Noe, Nov 15 2010

Edited by Max Alekseyev, Nov 19 2010

STATUS

approved

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Last modified September 24 15:40 EDT 2021. Contains 347643 sequences. (Running on oeis4.)