A227793 Numbers whose digital sum is a multiple of 5.

0, 5, 14, 19, 23, 28, 32, 37, 41, 46, 50, 55, 64, 69, 73, 78, 82, 87, 91, 96, 104, 109, 113, 118, 122, 127, 131, 136, 140, 145, 154, 159, 163, 168, 172, 177, 181, 186, 190, 195, 203, 208, 212, 217, 221, 226, 230, 235, 244, 249, 253, 258, 262, 267, 271, 276

Offset: 1

Author

Michel Marcus, Sep 23 2013

Keywords

• nonn
• base

Comments

Most first differences are 5, 9 and 4. First differences are strictly less than 10. First occurrences d of first difference a(i+1) - a(i) are for (d, i, a(i)) in {(5,1,0), (9,2,5), (4,4,19), (8,20,96), (3,60,299), (7,100, 997), (2,800,3999), (6, 2000, 9998), (1,10000,49999)}. - William Hitt, Apr 21 2014; comments modified by David A. Corneth, Jun 08 2016

a(10000) = 49999 is the smallest term that is congruent to 4 modulo 9. - Bruno Berselli, Feb 09 2016

Crossrefs

Cf. A007953.

Subsequences: A052219, A052224.

Programs

Magma

[n: n in [0..300] | IsZero(&+Intseq(n) mod 5)]; // Bruno Berselli, Sep 23 2013

Magma

[n: n in [0..300] | IsIntegral(&+Intseq(n)/5)];  // Bruno Berselli, Feb 09 2016

Mathematica

Select[Range[0, 280], IntegerQ[Total[IntegerDigits[#]]/5] &] (* Bruno Berselli, Feb 09 2016 *)

PARI

isok(n) = {if (n == 0, return (1)); digs = digits(n); return (sum(i=1, #digs, digs[i]) % 5 == 0);} \\ Michel Marcus, Sep 23 2013

PARI

a(n) = n--;m=10*(n\2);s=sumdigits(m);m+(4-(s-1)%5)+5*(n%2==1) \\ David A. Corneth, Jun 05 2016