A077506 Smallest n-digit triangular number beginning with n.

1, 21, 300, 4005, 50086, 600060, 7003153, 80004925, 900003951, 1000006281, 11000078650, 120000270151, 1300001532378, 14000004645256, 150000007349286, 1600000000287153, 17000000065300605, 180000000300000000, 1900000001049159015, 20000000001032428860

Offset

1,2

Links

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

Mathematica

sntn[x_]:=Module[{c=Ceiling[(Sqrt[1+8(x 10^(x-IntegerLength[x]))]-1)/2]}, (c(c+1))/2]; Array[sntn, 30] (* Harvey P. Dale, May 10 2021 *)

Prog

(Python)
from sympy import integer_nthroot
def a(n):
  target = 2 * int(str(n) + '0'*(n-len(str(n))))
  r, exact = integer_nthroot(target, 2)
  while r*(r+1)//2 >= target//2: r -= 1
  return (r+1)*(r+2)//2
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 28 2021

Crossrefs

Cf. A000217, A077507 (largest).

Sequence in context: A295377 A021604 A025935 * A007592 A019664 A019839

Adjacent sequences: A077503 A077504 A077505 * A077507 A077508 A077509

Keyword

base,nonn

Author

Amarnath Murthy, Nov 08 2002

Extensions

More terms from Sascha Kurz, Jan 04 2003

Status

approved