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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

K. D. Bajpai, May 15 2014

Keywords

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.

Examples

			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.

Links

Crossrefs

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

Programs

  • 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 &]
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