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 A062400 Smallest multiple of n with property that digits are even and each digit is two more (mod 10) than the previous digit; or 0 if no such multiple exists. 1
 2, 2, 6, 4, 80, 6, 46802, 8, 468, 80, 68024, 24, 468, 46802, 4680, 80, 68, 468, 6802, 80, 80246802468, 68024, 46, 24, 0, 468, 680246802, 80246802468, 680246802468, 4680, 24680246802468, 0, 680246802468024, 68, 802468024680, 468, 24680246802468, 6802 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If a(n) = 0, a(n*k) = 0 for any positive k. - Franklin T. Adams-Watters, Nov 03 2009 25 is impossible; its multiples end either with the digits 00 or 50. Multiples of 16 except 16 and 80 are impossible. Of the 625 multiples of 16 mod 10000, none are 246, 2468, 4680, 6802, or 8024. That leaves only 80 as a possible value for multiples of 16. It appears that the multiples of 16 and 25 are the only numbers for which a(n) = 0 - Franklin T. Adams-Watters, Nov 03 2009 LINKS Franklin T. Adams-Watters, Table of n, a(n) for n = 1..1000. EXAMPLE a(7) = 7*6686 = 46802 and this number has increasing larger even digits (mod 10). a(12) = 24 = 12*2 has increasing even digits. MATHEMATICA f[n_] := Block[{x = 0, a = IntegerDigits[n], i = 1}, l =Length[a]; While < l, If[ Mod[ a[[i]] + 2, 10] != a + 1]], x = 1]; i++ ]; Return[x]]; Dock = n; While[ Union[ even[ IntegerDigits[k]]] != {True} || Fmk] == 1, k += n]; Print[k], {n, 1, 20}] PROG (PARI) evenincr(n)=local(d, r); d=n%4*2+2; n\=4; r=0; for(k=0, n, r=r*10+(d+2*k)%10); r a(n)=if(n%25==0 || (n%16==0&80%n!=0), 0, k=0; while(evenincr(k)%n!=0, k++); evenincr(k)) /* This program will loop if the conjecture above is incorrect. */ CROSSREFS Sequence in context: A356187 A204991 A054516 * A064766 A019749 A209773 Adjacent sequences: A062397 A062398 A062399 * A062401 A062402 A062403 KEYWORD nonn,base,easy AUTHOR Amarnath Murthy, Jun 28 2001 EXTENSIONS Edited and extended by Robert G. Wilson v, Feb 22 2002 Edited and extended by Franklin T. Adams-Watters, Nov 03 2009 STATUS approved

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Last modified November 28 06:02 EST 2023. Contains 367394 sequences. (Running on oeis4.)