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 A353030 a(n) is the first emirp p such that there are exactly n unordered pairs (q,r) of emirps with p = q*r + q + r. 1
 13, 1439, 100799, 3548879, 14061599, 38342303, 120355199, 12555446399 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) is the first prime p such that the digit-reversal rev(p) of p is a prime and there are exactly n pairs (q,r) of primes such that q < r, rev(q) and rev(r) are primes, and p = q*r + q + r. From David A. Corneth, Jan 14 2023: (Start) a(8) <= 121347071999, a(9) <= 195271876799, a(10) <= 10175362797599, a(11) <= 17482966300799. For n >= 2, n == 3 (mod 4) and (n + 1)/4 has at least 2*n divisors. (End) LINKS Table of n, a(n) for n=0..7. David A. Corneth, Upper bounds on a(0)..a(30). EXAMPLE a(3) = 3548879 because 3548879 = 17*197159 + 17 + 197159 = 359*9857 + 359 + 9857 = 953*3719 + 953 + 3719 and 3548879, 17, 197159, 359, 9857, 953, 3719 are emirps. MAPLE revdigs:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc: isemirp:= proc(p) local r; if not isprime(p) then return false fi; r:= revdigs(p); r <> p and isprime(r) end proc: g:= proc(n) local p, q, t, count; count:= 0; for t in select(`<`, numtheory:-divisors(n+1), floor(sqrt(n+1))) do if isemirp(t-1) and isemirp((n+1)/t-1) then count:= count+1; fi od; count end proc: V:= Array(0..6): vcount:= 0: p:= 2: while vcount < 7 do p:= nextprime(p); d:= ilog10(p); p1:= floor(p/10^d); if p1=2 then p:= nextprime(3*10^d) elif member(p1, {4, 5, 6}) then p:= nextprime(7*10^d) elif p1=8 then p:= nextprime(9*10^d) fi; if isemirp(p) then v:= g(p); if V[v] = 0 then vcount:= vcount+1; V[v]:= p; fi; fi od: convert(V, list); CROSSREFS Cf. A006567, A352249. Sequence in context: A203369 A350305 A197097 * A064962 A242562 A201357 Adjacent sequences: A353027 A353028 A353029 * A353031 A353032 A353033 KEYWORD nonn,base,more AUTHOR J. M. Bergot and Robert Israel, Apr 18 2022 EXTENSIONS a(7) from David A. Corneth, Jan 14 2023 STATUS approved

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Last modified September 22 10:41 EDT 2023. Contains 365520 sequences. (Running on oeis4.)