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A088798 Numbers n that divide the concatenation of n-1, n-2 and n-3.

%I A088798 #8 Jun 08 2025 16:15:42
%S A088798 3,19,57,3276457,9829371,22997937,24687460011,24504559526049,
%T A088798 1152870338086169,3458611014258507,19831522709797616449,
%U A088798 54128285729329681609,59494568129392849347,61582096835687335289
%N A088798 Numbers n that divide the concatenation of n-1, n-2 and n-3.
%C A088798 Each member of this sequence also appears to be a divisor of the number formed when concatenating (n+1), (n+2) and (n+3) in that order. Each nonprime member of the terms above appears to be divisible by 3. Further note that apart from 3 itself, if a(n) is a prime, then 3 * a(n) also appears to be a member. 19*3=57, 3276457*3=9829371. More prime members would need to be found to test this.
%e A088798 a(2)=19 because 19 is a divisor of 181716. a(4)=3276457 because 3276457 is a divisor of 327645632764553276454.
%p A088798 prevcatOld := proc(n,t,o) local i,s; s := ""; for i from 1 to t do if o="a" then s := cat(convert(n-i,string),s) else s := cat(s,convert(n-i,string)) fi; od; parse(s) end; nextdivcat := proc(startAt,endAt,numTerms,catOrder) local i; for i from startAt to endAt while (prevcatOld(i,numTerms,catOrder) mod i > 0) do od; if i<=endAt then i else -1 fi; end; s := NULL; t := 2; for j from 1 to 10 do t := nextdivcat(t+1,23000000,3,"d"); s := s,t od; print(s);
%t A088798 Do[ If[ Mod[ FromDigits[ Join[ IntegerDigits[2n], IntegerDigits[2n - 1], IntegerDigits[2n - 2]]], (2n + 1)] == 0, Print[2n + 1]], {n, 1, 700000000}]
%Y A088798 Cf. A069860, A069862, A069871, A088797.
%K A088798 base,nonn
%O A088798 1,1
%A A088798 _Chuck Seggelin_, Oct 19 2003
%E A088798 Edited by _Robert G. Wilson v_, Oct 20 2003
%E A088798 More terms from _David Wasserman_, Aug 25 2005