A067270 Numbers m such that m-th triangular number (A000217) ends in m.
0, 1, 5, 25, 625, 9376, 90625, 890625, 7109376, 12890625, 212890625, 1787109376, 81787109376, 59918212890625, 259918212890625, 3740081787109376, 56259918212890625, 256259918212890625, 7743740081787109376
Offset: 1
Examples
The 5th triangular = 15 ends in 5, hence 5 is a term of the sequence.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..888
- Robert Dawson, On Some Sequences Related to Sums of Powers, J. Int. Seq., Vol. 21 (2018), Article 18.7.6.
Crossrefs
Programs
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Mathematica
(* a5=A018247 less the commas; a6=A018248 less the commas; *) b5 = FromDigits[ Reverse[ IntegerDigits[a5]]]; b6 = FromDigits[ Reverse[ IntegerDigits[a6]]]; f[0] = 1; f[n_] := Block[{c5 = Mod[b5, 10^n], c6 = Mod[b6, 10^n]}, If[ Mod[c5(c5 + 1)/2, 10^n] == c5, c5, c6]]; Union[ Table[ f[n], {n, 0, 20}]]
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Python
from itertools import count, islice from sympy.ntheory.modular import crt def A067270_gen(): # generator of terms a = 0 yield from (0,1) for n in count(0): if (b := int(min(crt(m:=(1<<(n+1),5**n),(0,1))[0], crt(m,(1,0))[0]))) > a: yield b a = b A067270_list = list(islice(A067270_gen(),15)) # Chai Wah Wu, Jul 25 2022
Extensions
Edited and extended by Robert G. Wilson v, Nov 20 2002
0 prepended by David A. Corneth, Aug 02 2018
Comments