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 A345410 a(n) is the least number that is the sum of an emirp and its reversal in exactly n ways. 1
 44, 1090, 10450, 5104, 88888, 10780, 289982, 299992, 482174, 478874, 868868, 499994, 1073270, 1087790, 1071070, 1069970, 10904990, 10794980, 1091090, 10892990, 1100000, 29955992, 1101100, 26688662, 31022002, 27599572, 46400354, 44688644, 29821792, 45289244, 30122092, 26988962 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Interchanging an emirp and its reversal is not counted as a different way. a(n) is the least number k such there are exactly n unordered pairs of distinct primes (p,p') such that p' is the digit reversal of p and p+p' = k. Are terms not divisible by 3? Amiram Eldar finds proof they are; A056964(n) = n + reverse(n) is divisible by 3 if and only if n is divisible by 3. But emirps are primes (other than 3) so they are not divisible by 3. - David A. Corneth, Jun 19 2021 LINKS David A. Corneth, Table of n, a(n) for n = 1..423 David A. Corneth, A few examples EXAMPLE a(3) = 10450 because 10450 = 1229+9221 = 1409+9041 = 3407+7043. MAPLE revdigs:= proc(n) local L, i; L:= convert(n, base, 10); add(L[-i]*10^(i-1), i=1..nops(L)) end proc: isemirp1:= proc(n) local r; if not isprime(n) then return false fi; r:= revdigs(n); r > n and isprime(r) end proc: E:= select(isemirp1, [seq(seq(seq(i*10^d+j, j=1..10^d-1, 2), i=[1, 3, 7, 9]), d=1..5)]): V:= sort(map(t -> t+revdigs(t), E)): N:= nops(V): W:= Vector(16): i:= 1: while i < N do for j from 1 to N-i while V[i+j]=V[i] do od: if j <= 16 and W[j] = 0 then W[j]:= V[i] fi;   i:= i+j; od: convert(W, list); PROG (Python) from itertools import product from collections import Counter from sympy import isprime, nextprime def epgen(start=1, end=float('inf')): # generates unique emirp/prime pairs     digits = 2     while True:       for first in "1379":         for last in "1379":           if last < first: continue           for mid in product("0123456789", repeat=digits-2):             strp = first + "".join(mid) + last             revstrp = strp[::-1]             if strp >= revstrp: continue             p = int(strp)             if p > end: return             revp = int(strp[::-1])             if isprime(p) and isprime(revp): yield (p, revp)       digits += 1 def aupto(lim):     alst = []     c = Counter(sum(ep) for ep in epgen(1, lim) if sum(ep) <= lim)     r = set(c.values())     for i in range(1, max(r)+1):         if i in r: alst.append(min(s for s in c if c[s] == i))         else: break     return alst print(aupto(11*10**5)) # Michael S. Branicky, Jun 19 2021 CROSSREFS Cf. A006567, A345408, A345409. Sequence in context: A004423 A238601 A172978 * A114170 A130645 A004340 Adjacent sequences:  A345406 A345408 A345409 * A345411 A345412 A345413 KEYWORD nonn,base AUTHOR J. M. Bergot and Robert Israel, Jun 18 2021 EXTENSIONS More terms from David A. Corneth, Jun 18 2021 STATUS approved

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Last modified September 22 09:47 EDT 2021. Contains 347606 sequences. (Running on oeis4.)