cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

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

Views

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 &]

A261560 Semiprimes sp such that (sum of digits of (sp)) + (product of digits of (sp)) is also semiprime.

Original entry on oeis.org

14, 33, 38, 39, 46, 49, 55, 69, 74, 82, 86, 93, 94, 111, 121, 122, 141, 142, 146, 161, 166, 202, 214, 221, 226, 247, 249, 254, 259, 262, 274, 278, 287, 295, 301, 303, 323, 334, 346, 386, 411, 427, 445, 454, 458, 469, 485, 489, 501, 505, 529, 542, 565, 586, 589
Offset: 1

Views

Author

K. D. Bajpai, Aug 24 2015

Keywords

Examples

			a(1) = 14 = (2 * 7), is semiprime. (1+4) + (1*4) = 9 = (3 * 3) is also semiprime.
a(3) = 38 = (2 * 19), is semiprime. (3+8) + (3*8) = 35 = (7 * 5) is also semiprime.

Links

Crossrefs

Cf. A001358, A061762, A118688, A118689, A118690.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [11..300] | IsSemiprime(n) and IsSemiprime(k) where k is (&+Intseq(n) + &*Intseq(n))];
  • Maple
    with(numtheory): select(n -> bigomega(n)=2 and bigomega( add(d, d=convert(n, base, 10)) + mul(d, d=convert(n, base, 10)) ) = 2, [seq(n, n=1..300)]);
  • Mathematica
    Select[Range[2000], PrimeOmega[#] == 2 && PrimeOmega[(Plus @@ IntegerDigits[#]) + (Times @@ IntegerDigits[#])] == 2 &]
  • PARI
    for(n = 1, 300, d = digits(n); pd = prod(i = 1, #d, d[i]); if(bigomega(n)==2 && bigomega(sumdigits(n) + pd)==2, print1(n,", ")));

A357896 Additive triprimes.

Original entry on oeis.org

8, 44, 66, 75, 99, 116, 125, 138, 147, 165, 170, 174, 242, 246, 255, 273, 279, 282, 318, 332, 345, 354, 363, 369, 387, 404, 426, 435, 477, 507, 530, 534, 549, 561, 578, 596, 602, 606, 615, 639, 642, 651, 657, 668, 705, 710, 741, 747, 822, 873, 903, 909, 927, 938, 956, 963, 981, 1025, 1034, 1038, 1052, 1065, 1070, 1074
Offset: 1

Views

Author

Zak Seidov, Oct 18 2022

Keywords

Comments

Triprimes for which the sum of the digits is also a triprime.

Examples

			75 = 3*5*5 and 5 + 7 = 12 = 2*2*3 (both are product of 3 primes).

Crossrefs

Cf. A007953, A014612, A046704, A118688.

Programs

  • Mathematica
    s = Select[Range[8, 1500], 3 == PrimeOmega[#] &]; s = Select[s, 3 == PrimeOmega[Total[IntegerDigits[#]]] &]
  • PARI
    istp(k) = bigomega(k)==3; \\ A014612
isok(k) = istp(k) && istp(sumdigits(k)); \\ Michel Marcus, Nov 02 2022
Showing 1-3 of 3 results.

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