The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A358482 a(n) is the first prime p such that, if q is the next prime, (p*q+p+q)/5^n is a prime. 0
 2, 7, 1847, 90793, 139313, 1790293, 3834043, 5521543, 24996487, 2062865293, 5555052793, 12111965183, 95460776921, 6045070151921, 10204150316653, 70501997496487, 442748358250633, 368313674465183, 2935956099058987, 10360552690003447, 120999670013476223, 1820610211470152737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Suggested in an email by J. M. Bergot. For n >= 1, a(n) has the form k * 5^n + x, for some k >= 0, where x is a solution to the modular quadratic equation x^2 + (d+2)*x + d == 0 (mod 5^n), where d = q-p. - Daniel Suteu, Dec 28 2022 LINKS Table of n, a(n) for n=0..21. EXAMPLE a(2) = 1847 because 1847 is prime, the next prime is 1861, 1847*1861 + 1847 + 1861 = 3440975 = 5^2 * 137639 where 137639 is prime, and no smaller prime works. MAPLE V:= Array(0..8): q:= 2: count:= 0: while count < 9 do p:= q; q:= nextprime(q); t:= p*q+p+q; k:= padic:-ordp(t, 5); if V[k] = 0 and isprime(t/5^k) then V[k]:= p; count:= count+1 fi od: convert(V, list); CROSSREFS Cf. A000351, A002386, A126148. Sequence in context: A128847 A123180 A138198 * A320505 A144836 A174308 Adjacent sequences: A358479 A358480 A358481 * A358483 A358484 A358485 KEYWORD nonn AUTHOR Robert Israel, Dec 25 2022 EXTENSIONS a(11) from Michael S. Branicky, Dec 26 2022 a(12)-a(15) from David A. Corneth, Dec 26 2022 a(16) from Martin Ehrenstein, Dec 27 2022 a(17)-a(21) from Daniel Suteu, Dec 28 2022 STATUS approved

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

Last modified May 18 23:43 EDT 2024. Contains 372666 sequences. (Running on oeis4.)