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

Author

Amarnath Murthy, Mar 06 2002

Keywords

• base
• easy
• nonn

Examples

			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
		

Links

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

Crossrefs

Cf. A000217, A062688.

Programs

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 *)

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])A068808,tri(k),y);y++)); A068808 \\ Edward Jiang, Sep 04 2014

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