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

3, 19, 57, 3276457, 9829371, 22997937, 24687460011, 24504559526049, 1152870338086169, 3458611014258507, 19831522709797616449, 54128285729329681609, 59494568129392849347, 61582096835687335289

Offset: 1

Author

Chuck Seggelin, Oct 19 2003

Keywords

• base
• nonn

Comments

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.

Examples

			a(2)=19 because 19 is a divisor of 181716. a(4)=3276457 because 3276457 is a divisor of 327645632764553276454.
		

Crossrefs

Cf. A069860, A069862, A069871, A088797.

Programs

Maple

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);

Mathematica

Do[ If[ Mod[ FromDigits[ Join[ IntegerDigits[2n], IntegerDigits[2n - 1], IntegerDigits[2n - 2]]], (2n + 1)] == 0, Print[2n + 1]], {n, 1, 700000000}]

Extensions

Edited by Robert G. Wilson v, Oct 20 2003

More terms from David Wasserman, Aug 25 2005