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 A267939 Number x = concat(MSD(x),b), where MSD = A000030 stands for Most Significant Digit, such that MSD(x)*b is equal to the reverse of x. 2
 351, 621, 886, 920781, 3524751, 338752611, 35247524751, 920780120781, 920879219781, 3387524752611, 3526124738751, 338738752612611, 352475247524751, 33875247524752611, 35247387526124751, 35261247524738751, 920780120780120781, 920780219879120781, 920879120780219781, 920879219879219781 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If we consider numbers x = concat(a,b), where a has two digits, such that a*b is equal to the reverse of x, the first terms are 425322, 44235301, 119910901, ... Terms of the form 3(5247)*51, i.e. 351, 3524751, 35247524751, ..., form an infinite subsequence. - Robert Israel, Jan 28 2016 Other infinite sequences of terms include 92078(012078)*1 and 33875(2475)*2611. - Robert Israel, Jan 31 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..415 EXAMPLE 3*51 = 153; 6*21 = 126; 3*524751 = 1574253. MAPLE T:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end: P:=proc(q) local a, b, n; for n from 1 to q do a:=n mod 10; b:=trunc(n/10^ilog10(n)); if (a=1 and b>1) or (a=6 and (b=2 or b=4 or b=6 or b=8)) or (b=5 and (a=3 or a=5 or a=7 or a=9)) then if T(n)=b*(n mod 10^ilog10(n)) then print(n); fi; fi; od; end: P(10^10); # alternative: N:= 20: # to get all terms with at most N digits. extend:= proc(d, psol, eqs)   local peqs, cvars, bvars, ncs, res, T, cs, ceqs, sol, svals;   peqs:= subs(psol, eqs);   cvars, bvars:= selectremove(t -> op(0, t) = 'c', indets(peqs));   ncs:= nops(cvars);   res:= NULL;   if ncs >= 1 then     T:= combinat:-cartprod([[\$0..d-1]\$ncs]);     while not T[finished] do       cs:= T[nextvalue]();       cs:= seq(cvars[i]=cs[i], i=1..ncs);       ceqs:= subs(cs, peqs);       sol:= solve(ceqs, bvars); svals:= map(rhs, sol);       if indets(svals) <> {} then error("Oops: %1", svals) fi;       if svals::set(nonnegint) and max(svals) <= 9 then         res:= res, [op(psol), cs, op(sol)];       fi     od   else     sol:= solve(peqs, bvars);     svals:= map(rhs, sol);     if indets(svals) <> {} then error("Oops: %1", svals) fi;     if svals::set(nonnegint) and max(svals) <= 9 then         res:= [op(psol), op(sol)];     fi   fi;   [res] end proc: G:= proc(d, n)      local eqs, i, rs, b0s;      eqs:= [d*b[0] - d - 10*c[0],             seq(d*b[i]+c[i-1] - b[n-i] - 10*c[i], i=1..n-2),             d*b[n-1] + c[n-2] - b[1] - 10*b[0]];      b0s:= [msolve(eqs[1] mod 10, 10)];      rs:= select(t -> (map(rhs, t))::set(nonnegint),          map(t -> t union solve(eval(eqs[1], t), {c[0]}), b0s));      for i from 1 to floor(n/2) do         rs:= map(s -> op(extend(d, s, {eqs[i+1], eqs[-i]})), rs);      od;      sort(map(s -> d*10^n + subs(s, add(10^i*b[i], i=0..n-1)), rs)); end proc: A:= NULL; for n from 2 to N-1 do   for d from 3 to 9 do     res:= G(d, n);     if res <> [] then       A:= A, op(res);     fi   od od: A; # Robert Israel, Feb 01 2016 MATHEMATICA Select[Range@ 4000000, First[#] FromDigits@ Rest@ # == FromDigits@ Reverse@ # &@ IntegerDigits@ # &] (* Michael De Vlieger, Jan 29 2016 *) CROSSREFS Cf. A000030, A004086. Sequence in context: A261640 A292990 A281555 * A092374 A273255 A264426 Adjacent sequences:  A267936 A267937 A267938 * A267940 A267941 A267942 KEYWORD base,nonn AUTHOR Paolo P. Lava, Jan 22 2016 EXTENSIONS a(7) to a(20) from Robert Israel, Feb 01 2016 STATUS approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)