The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A072344 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A072344

a(n) = the least natural number k such that k*phi(n) + 1 is prime.
(history; published version)

#7 by Bruno Berselli at Wed Aug 23 06:06:35 EDT 2017

STATUS

proposed

approved

#6 by Antti Karttunen at Tue Aug 22 14:46:21 EDT 2017

STATUS

editing

proposed

#5 by Antti Karttunen at Tue Aug 22 14:44:08 EDT 2017

LINKS

Antti Karttunen, <a href="/A072344/b072344.txt">Table of n, a(n) for n = 1..10000</a>

#4 by Antti Karttunen at Tue Aug 22 14:42:53 EDT 2017

FORMULA

a(n) = A034693(A000010(n)). - Antti Karttunen, Aug 22 2017

PROG

(PARI)

A034693(n) = { my(k=1); while(!isprime(1+(k*n)), k++); k; };

A072344(n) = A034693(eulerphi(n)); \\ Antti Karttunen, Aug 22 2017

CROSSREFS

Cf. A000010, A034693, A072917.

STATUS

approved

editing

#3 by N. J. A. Sloane at Tue Feb 11 19:05:29 EST 2014

AUTHOR

_Joseph L. Pe (joseph_l_pe(AT)hotmail.com), _, Jul 16 2002

Discussion

Tue Feb 11

19:05

OEIS Server: https://oeis.org/edit/global/2119

#2 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

phi(35) = 24, and the least natural number k such that 24 k + 1 is prime is k = 3; so a(35) = 3.

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

a(n) = the least natural number k such that k*phi(n) + 1 is prime.

DATA

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 3, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 2, 1, 1, 3, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 2

OFFSET

1,15

EXAMPLE

phi(35) = 24, and the least natural number k such that 24 k + 1 is prime is k = 3; so a(35) = 3.

MATHEMATICA

f[n_] := Module[{i}, i = 0; While[ ! PrimeQ[i*EulerPhi[n] + 1], i++ ]; i]; Table[f[i], {i, 1, 150}]

KEYWORD

nonn

AUTHOR

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jul 16 2002

STATUS

approved