A068808 Triangular numbers with strictly increasing sum of digits.

1, 3, 6, 28, 66, 78, 378, 496, 1596, 5778, 5995, 8778, 47895, 58996, 196878, 468996, 887778, 1788886, 4896885, 5897895, 13999986, 15997996, 38997696, 88877778, 179977878, 189978778, 398988876, 686999778, 1699998895, 5779898886, 9876799878, 38689969878, 39689699896, 67898888778, 89996788896, 299789989975

Offset

1,2

Links

K. D. Bajpai, Table of n, a(n) for n = 1..55

Example

a(4) = 28 = 7 * (7 + 1) / 2, which is 7th triangular number with sum of digits = 2 + 8 = 10.  a(5) = 66 = 11 * (11 + 1) / 2, which is 11th triangular number with sum of digits = 6 + 6 = 12. Since  12 > 10, 28 and 66 are in list. - K. D. Bajpai, Sep 04 2014

Maple

dig := X->convert((convert(X, base, 10)), `+`); T := k->k*(k+1)/2; S := k->seq(dig(T(i)), i=1..k-1); seq(`if`(n>1 and dig(T(n))>max(S(n)), T(n), printf("")), n=1..2000);

Mathematica

t = {}; s = 0; Do[If[(x = Total[IntegerDigits[y = n*(n + 1)/2]]) > s, AppendTo[t, y]; s = x], {n, 120000}]; t (* Jayanta Basu, Aug 06 2013 *)

Prog

(PARI)
tri(n)=n*(n+1)/2;
A068808=List; listput(A068808, 1, 1);
y=2; for(k=1, 100000, if(sumdigits(Vec(A068808)[y-1])<sumdigits(tri(k)), listput(A068808, tri(k), y); y++)); A068808 \\ Edward Jiang, Sep 04 2014

Crossrefs

Cf. A000217, A062688.

Sequence in context: A075088 A102428 A128056 * A068133 A370668 A220823

Adjacent sequences: A068805 A068806 A068807 * A068809 A068810 A068811

Keyword

base,easy,nonn

Author

Amarnath Murthy, Mar 06 2002

Extensions

More terms from Francois Jooste (phukraut(AT)hotmail.com), Mar 10 2002

More terms from Sascha Kurz, Mar 27 2002

a(31) to a(33) from K. D. Bajpai, Sep 04 2014

a(34) to a(36) from Robert Israel, Sep 04 2014

Status

approved