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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110358 Beginning with 3, the least prime which is the product of one or more previous terms + 2. 1
3, 5, 7, 17, 19, 23, 37, 53, 59, 61, 71, 73, 97, 107, 109, 113, 163, 179, 181, 257, 293, 307, 347, 349, 359, 367, 373, 401, 439, 487, 491, 499, 547, 557, 631, 751, 773, 797, 853, 881, 883, 887, 907, 971, 1009, 1039, 1049, 1051, 1097, 1103, 1123, 1283, 1297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: The sequence is infinite.

Subbarao & Yip prove that if there is an integer m such that the equation Phi_2(x) = m has a unique solution, where Phi_2 is the 2nd Schemmel totient function (A058026), then x == 0(mod a(n)^2) for each term in this sequence. They conjectured an analog to Carmichael's conjecture, that this equation has no unique solution to any integer m, and prove that any counter-example to this conjecture is > 10^120000, a bound calculated from the first 10000 terms of this sequence. A proof that this sequence is infinite would prove the conjecture. - Amiram Eldar, Mar 25 2017

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

M. V. Subbarao and L. W. Yip, Carmichael's conjecture and some analogues, Théorie des nombres/Number Theory: Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987, Jean M. de Koninck and Claude Levesque, eds., Walter de Gruyter, 1989, pp. 928-941.

EXAMPLE

After 3, 5 and 7 the next term is 3*5 +2 = 17, then 17+2 = 19, then 3*7 +2 = 23, then 5*7 +2 = 37, etc.

MATHEMATICA

L={3}; p=3; While[Length[L] < 100, p = NextPrime@p; If[SquareFreeQ[p - 2] && SubsetQ[L, First /@ FactorInteger[p - 2]], AppendTo[L, p]]]; L (* Giovanni Resta, Mar 25 2017 *)

CROSSREFS

Cf. A058026.

Sequence in context: A276044 A114265 A258195 * A038971 A210479 A045400

Adjacent sequences:  A110355 A110356 A110357 * A110359 A110360 A110361

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jul 23 2005

EXTENSIONS

More terms from John Pammer (jcp5027(AT)psu.edu), Oct 10 2005

Corrected and extended by Joshua Zucker, May 08 2006

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 October 23 12:04 EDT 2019. Contains 328345 sequences. (Running on oeis4.)