A242454 Triangular numbers T such that sum of digits of T is semiprime.

6, 15, 28, 36, 45, 55, 78, 91, 105, 136, 153, 171, 190, 231, 253, 276, 325, 351, 406, 465, 528, 630, 703, 780, 820, 861, 1035, 1081, 1176, 1225, 1275, 1431, 1540, 1596, 1653, 1711, 1770, 2016, 2080, 2211, 2346, 2701, 2775, 2850, 3003, 3160, 3240, 3321, 3403

Offset

1,1

Comments

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

Triangular numbers with digital sum = p * q, where p and q are primes.

Links

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

Example

a(2) = 15 = 5*(5+1)/2: 1+5 = 6 = 2 * 3 is semiprime.
a(3) = 28 = 7*(7+1)/2: 2+8 = 10 = 2 * 5 is semiprime.

Maple

with(numtheory): A242454:= proc()local a, b; a:=x*(x+1)/2; b:=add( i, i = convert((a), base, 10))(a); if  bigomega(b)=2 then  RETURN (a); fi; end: seq(A242454 (), x=1..100);

Mathematica

Select[Table[n*(n+1)/2, {n, 200}], PrimeOmega[Sum[DigitCount[#][[i]]*i, {i, 1, 9}]] == 2 &]

Crossrefs

Cf. A000217, A001358, A158195, A118688, A242343.

Sequence in context: A063525 A335267 A349476 * A161777 A117519 A091012

Adjacent sequences: A242451 A242452 A242453 * A242455 A242456 A242457

Keyword

nonn,base,less

Author

K. D. Bajpai, May 15 2014

Status

approved