A242831 Triangular numbers T such that sum of the factorials of digits of T is prime.

10, 21, 136, 153, 351, 630, 780, 3403, 3570, 5671, 6441, 6670, 7503, 9870, 10011, 13366, 14535, 16653, 20301, 23220, 33153, 34716, 36046, 36315, 37950, 43660, 46360, 56616, 66430, 93096, 93961, 95703, 112101, 139656, 144453, 159895, 166753, 169653, 187578

Offset: 1

Author

K. D. Bajpai, May 23 2014

Keywords

• nonn
• base

Comments

The n-th triangular number T(n) = n * (n+1)/2.

Intersection of A165451 and A000217.

Examples

			16*(16+1)/2 = 136 is triangular number. 1! + 3! + 6! = 727 which is prime. Hence 136 appears in the sequence.
35*(35+1)/2 = 630 is triangular number. 6! + 3! + 0! = 727 which is prime. Hence 630 appears in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A061602, A165451.

Programs

Maple

A242831:= proc()  if isprime(add( i!,i = convert((x*(x+1)/2), base, 10))(x*(x+1)/2))then RETURN ((x*(x+1)/2)); fi; end: seq(A242831 (), x=1..1000);