A318273 Numbers with digits in nondecreasing order such that additive and multiplicative digital roots coincide.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 123, 137, 139, 168, 179, 188, 233, 267, 299, 346, 389, 899, 1124, 1157, 1347, 1355, 1469, 1779, 1788, 2236, 2346, 2348, 2778, 3335, 3779, 11126, 11133, 11148, 11177, 11222, 11238, 11279, 11339, 11369, 11579, 11666, 11677, 11679, 11699

Offset

1,3

Comments

A299690 can be used to find terms for this sequence below some bound by prepending ones to terms while staying below that bound so the additive and multiplicative root that term matches.

For example, 27 is in A299690 and has multiplicative root 4. 27 has the additive root 9. Prepending 4 ones gives the number 111127 which has multiplicative root 4, the same as 27 has, but it also has an additive root of 4. Furthermore, the digits are in nondecreasing order hence is in this sequence.

Links

Table of n, a(n) for n=1..50.

Prog

(PARI) is(n) = my(cn=n); d=digits(n); if(d!=vecsort(d), return(0)); while(cn>9, d=digits(cn); cn=prod(i=1, #d, d[i])); cn-1 == (n-1)%9 || n == 0

Crossrefs

Cf. A009994, A010888, A031347, A064702, A277061, A299690.

Sequence in context: A064702 A034710 A305257 * A061672 A272814 A322516

Adjacent sequences: A318270 A318271 A318272 * A318274 A318275 A318276

Keyword

nonn,base

Author

David A. Corneth, Aug 23 2018

Status

approved