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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: A259882 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 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)