A256884 Numbers divisible by prime(d+1) for each digit d of their base-4 representation.

0, 10, 21, 40, 63, 84, 90, 105, 130, 140, 150, 160, 165, 170, 175, 210, 252, 276, 324, 330, 336, 345, 360, 390, 405, 420, 520, 560, 600, 630, 640, 650, 660, 680, 700, 735, 770, 840, 861, 910, 1008, 1044, 1050, 1092, 1104, 1110, 1170, 1260, 1284, 1290, 1296, 1320, 1344, 1350, 1365, 1380, 1407, 1410, 1440, 1470, 1533, 1560, 1620

Offset

1,2

Comments

The base-4 variant of A256882, A256883, A256865, ..., A256870 in bases 2, ..., 10.

A variant of A256874 where digits 0 are forbidden and divisibility by prime(d) is required.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

0 is divisible by prime(0+1)=2.
10 = 22_4 and is divisible by prime(2+1)=5.
n = 1, 2, 3 are not divisible by prime(n+1) = 3, 5, 7; nor are 4=10_4, 5=11_4, and 7=13_4 divisible by prime(1+1) = 3; nor are 6=12_4, 8=20_4, 9=21_4 divisible by prime(2+1)=5.

Mathematica

Select[Range[0, 2000], AllTrue[#/(Prime[#+1]&/@IntegerDigits[#, 4]), IntegerQ]&] (* Harvey P. Dale, Mar 13 2025 *)

Prog

(PARI) is(n, b=4)=!for(i=1, #d=Set(digits(n, b)), n%prime(d[i]+1)&&return)

Crossrefs

Cf. A256882, A256883, A256865-A256870, A256874-A256879, A256786.

Sequence in context: A060852 A345962 A195142 * A089584 A192743 A280435

Adjacent sequences: A256881 A256882 A256883 * A256885 A256886 A256887

Keyword

nonn,base

Author

M. F. Hasler, Apr 11 2015

Status

approved