A330981 Remodd numbers: having an odd remainder modulo all of their digits, digit 0 forbidden.

43, 47, 73, 87, 223, 227, 253, 267, 283, 289, 337, 343, 349, 367, 379, 397, 433, 439, 463, 467, 469, 477, 489, 493, 523, 553, 583, 643, 647, 649, 669, 673, 677, 687, 689, 733, 747, 787, 799, 823, 827, 829, 849, 853, 869, 883, 887, 889, 943, 997

Offset: 1

Author

Eric Angelini and M. F. Hasler, Jan 05 2020

Keywords

• nonn
• base

Comments

No term may have a digit 0 or 1, therefore the asymptotic density is zero and would be so even if the definition is changed to "digits 0 are allowed but ignored", since pandigital numbers A171102 have asymptotic density 1.

Does not contain any remeven number (A330982), thus in particular none of A010785 (repdigits) or its superset A034838 (divisible by all digits) or A014263 (only even digits). Also no multiples of 2 or 5 (A005843 or A008587) which are even modulo the last digit (unless it is 0), so all terms end in 3, 7 or 9.

Contains the infinite subsequence (43, 433, 4333, ...), but after {47, 477, 4777} not 47777 = 6825*7 + 2, and after {73, 733} not 7333 = 1047*7 + 4, and after {87, 887} not 8887 = 1269*7 + 4.

The first term which contains the digits 2..9 is a(784795) = 224567983. - Giovanni Resta, Jan 07 2020

Examples

			43 is in the sequence because 43 mod 4 = 3 and 43 mod 3 = 1 both are odd.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Angelini, Remeven numbers, SeqFan list, Jan 05 2020.

Crossrefs

Cf. A330982 (remeven numbers).

Cf. A171102 (pandigitals), A010785 (repdigits), A014263 (only even digits), A034838 (divisible by all digits).

Programs

Magma

[k:k in [1..1000]|not 0 in Intseq(k) and forall{d:d in Intseq(k)|IsOdd(k mod d)}]; // Marius A. Burtea, Jan 07 2020

PARI

select( {is(n, d=Set(digits(n)))=d[1]&&!for(j=1,#d, bittest(n%d[j],0)||return)}, [1..2000])