login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121091 Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime. 3
7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, 5613125740675652943160572913465695837595324940170321, 371281, 919 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(19) = 19^1607 - 18^1607, which is too large to include. It has 2055 decimal digits. See A062585(1) = 1607.

a(20)-a(21) = {723901, 8005616640331026125580781}. a(n) is currently known for all n up to n = 96. Corresponding smallest odd primes p such that (n+1)^p - n^p is prime are listed in A125713(n) = {3,3,3,3,5,3,7,7,3,3,3,17,3,3,43,5,3,10957,5,19,127,229,3,3,3,13,3,3,149,3,5,3,23,3,5,83,3,3,37,7,3,3,37,5,3,5,58543,...}. a(n+1) = A065013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, ...} = A047845(n) = (n-1)/2, where n runs through odd nonprimes (A014076), for n>1.

LINKS

Table of n, a(n) for n=2..18.

FORMULA

a(n) = n^A125713(n) - (n-1)^A125713(n).

CROSSREFS

Cf. A121620, A000043, A058765, A121616, A121618.

Cf. A125713 = Smallest odd prime p such that (n+1)^p - n^p is prime. Cf. A065913 = Smallest prime of form (n+1)^k - n^k. Cf. A058013 = Smallest prime p such that (n+1)^p - n^p is prime. Cf. A047845, A014076.

Cf. A062585 = numbers n such that k^n - (k-1)^n is prime, where k is 19. Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Sequence in context: A155361 A155315 A155323 * A213489 A288021 A155394

Adjacent sequences:  A121088 A121089 A121090 * A121092 A121093 A121094

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Aug 11 2006, revised Dec 01 2006, Feb 15 2007

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 December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)