OFFSET
1,2
COMMENTS
Are all terms of the sequence bigger than 1 divisible by 3? I conjecture that 1 and 15 are the only terms for which (product of decimal digits of t(n)) = n.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..45 (all terms < 10^49. n = 1..31 from Sean A. Irvine, n = 32..35 from Giovanni Resta.)
C. Pomerance and Ch. Spicer, Proof of the Sheldon Conjecture.
EXAMPLE
For n = 30, t(30) = 465, product of decimal digits of t(30) = 4*6*5 = 120, product of decimal digits of t(n) / n = 120 / 30 = 4 so t(30) = 465 is in the sequence.
MATHEMATICA
idx = Select[Range[100000], Product[j, {j, IntegerDigits[#*(# + 1)/2]}] != 0 && Divisible[Product[j, {j, IntegerDigits[#*(# + 1)/2]}], #] &]; idx*(idx + 1)/2 (* Vaclav Kotesovec, Apr 30 2019 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Ctibor O. Zizka, Apr 30 2019
EXTENSIONS
More terms from Vaclav Kotesovec, Apr 30 2019
a(26)-a(27) from Chai Wah Wu, May 01 2019
STATUS
approved