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 A258336 Least solution of the equation x' = x + p for increasing values of p, where x' is the arithmetic derivative of x and p is an odd prime. a(n)= -1 if no such solution exists. 1
 18, 1554, 53922, 726, 1218, 3230934, 966, 798, 546, 462, 210, 330, 390, 510, 690, 870, 930, 1110, 1230, 1290, 748146, 1590, 1770, 2010, 2130, 2190, 10010, 2370, 2490, 2910, 3030, 3210, 3270, 325374, 16288662, 3810 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS First possible values without solutions are a(130), a(311), a(328), a(403) ... If they exist, a(38), a(51) > 7*10^11. a(40) = 53086075098, a(43) = 2205467286, a(59) = 1343266518. - Giovanni Resta, Jun 08 2015 From Hiroaki Yamanouchi, Aug 26 2015: (Start) a(130) > 5*10^13. a(38) <= 6757220092414242, a(82) <= 60382338056274, a(86) <= 4904019996019293138, a(100) <= 20288582235746170309362, a(103) <= 103153074623970054, a(185) <= 359626712451821152206, a(236) <= 41507154995420198557374 and a(378) <= 19746050339765838. a(51) = 49441344782046, a(70) = 487059258, a(88) = 701726466, a(91) = 2192479278, a(116) = 1835382005358, a(126) = 64331242458, a(133) = 2179114806, a(141) = 23383324866 and a(142) = 2175820746. (End) LINKS Table of n, a(n) for n=2..37. Paolo P. Lava, Solutions for the first 100 odd primes (-1 if no solution has been detected) EXAMPLE a(2) = 18 because the second prime is 3 and the solutions of the equation x' = x + 3 are 18, 315, ... where 18 is the least one. a(3) = 1554 because the third prime is 5 and the solutions of the equation x' = x + 5 are 1554, 27950, ... where 1554 is the least one. MAPLE with(numtheory); P:=proc(q) local b, c, n, p; for c from 2 to q do b:=ithprime(c); for n from 1 to q do if n+b=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]) then print(n); break; fi; od; od; end: P(10^9); PROG (PARI) der(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); a(n) = {k=1; p=prime(n); while(der(k) != k+p, k++); k; } \\ Michel Marcus, Aug 28 2015 CROSSREFS Cf. A000040, A003415. Sequence in context: A160252 A276015 A210823 * A211310 A160307 A003030 Adjacent sequences: A258333 A258334 A258335 * A258337 A258338 A258339 KEYWORD nonn,more AUTHOR Paolo P. Lava, May 27 2015 STATUS approved

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Last modified April 20 02:51 EDT 2024. Contains 371798 sequences. (Running on oeis4.)