A115670 -id:A115670 - cp's OEIS frontend

A182180 Semiprimes that become prime when their digits are sorted into nonincreasing order.

14, 34, 35, 38, 118, 119, 121, 133, 134, 142, 143, 145, 146, 166, 194, 214, 215, 218, 314, 334, 341, 346, 358, 361, 365, 377, 386, 395, 398, 413, 415, 437, 451, 473, 514, 517, 538, 583, 614, 634, 635, 671, 734, 737, 778, 779, 791, 799, 818, 835, 838, 878, 893

Offset: 1

Jonathan Vos Post, Apr 23 2012

Suggested by Kevin L. Schwartz.

			a(10) = 121 = 11*11, which becomes the prime 211 when its digits are sorted into nonincreasing order.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A000040, A001358, A115670 Semiprimes (A001358) whose digit reversal is prime, A182150 Semiprimes that are also semiprime when their digits are sorted into nondecreasing order.

h:= proc(m) local k; for k from m+1 while isprime(k) or
            add(i[2], i=ifactors(k)[2])<>2 do od; k
    end:
a:= proc(n) option remember; local k;
      k:= h(a(n-1));
      do if isprime(parse(cat(sort(convert(k, base, 10), `>`)[])))
            then return k else k:=h(k) fi
      od
    end: a(0):=0:
seq(a(n), n=1..80);  # Alois P. Heinz, Apr 23 2012

More terms from Alois P. Heinz, Apr 23 2012

A264815 Semirps: a semirp (or semi-r-p) is a semiprime r*p with r and p both reversed primes.

Original entry on oeis.org

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 39, 49, 51, 55, 62, 65, 74, 77, 85, 91, 93, 111, 119, 121, 142, 143, 146, 155, 158, 169, 185, 187, 194, 202, 213, 214, 217, 219, 221, 226, 237, 259, 262, 289, 291, 298, 302, 303, 314, 321, 334, 339, 341, 355

Offset: 1

Danny Rorabaugh, Nov 25 2015

A semiprime (A001358) is the product of two prime, not necessarily distinct. A semiprime is in this list if those two primes (A000040) are reversed primes (A004087).

Since A007500 is the intersection of A000040 and A004087, this sequence is also the sorted list of all r*p with r and p in A007500.

			9 is in the list because 9 = 3*3 is a semiprime and reverse(3) = 3 is prime.
143 is in the list because 143 = 11*13 is a semiprime and both reverse(11) = 11 and reverse(13) = 31 are prime.

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Cf. A001358, A006567, A007500, A097393, A109019, A115670.

With[{nn=250},Take[Union[Times@@@Select[Tuples[IntegerReverse/@Prime[Range[nn]],2],AllTrue[#,PrimeQ]&]],60]] (* Harvey P. Dale, Apr 27 2025 *)

reverse = lambda n: sum([10^i*int(str(n)[i]) for i in range(len(str(n)))])
def is_semirp(n):
  F = factor(n)
  if sum([f[1] for f in F])==2:
    r, p = F[0][0], F[-1][0]
    if is_prime(reverse(r)) and is_prime(reverse(p)): return True
[a for a in range(1,356) if is_semirp(a)] # Danny Rorabaugh, Nov 25 2015

[A007500]^2, sorted.

A368238 Semiprimes whose reversal is a prime, ordered by the prime.

Original entry on oeis.org

91, 14, 34, 74, 35, 95, 38, 301, 901, 721, 731, 361, 371, 391, 791, 922, 142, 362, 382, 703, 713, 133, 943, 763, 973, 793, 914, 134, 334, 934, 974, 194, 305, 905, 145, 745, 755, 365, 965, 785, 395, 995, 106, 706, 146, 346, 746, 166, 386, 917, 377, 118, 358, 758, 958, 778, 119, 749, 779, 799, 3101

Offset: 1

Zak Seidov and Robert Israel, Dec 18 2023

			a(4) = 74 because A115670(4) = 47 is the 4th prime whose reversal is a semiprime, and 74 is that reversal.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001358, A004086, A085778, A115670.

rev:= proc(n) local L,i;
       L:= convert(n,base,10);
       add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
map(rev, select(p -> isprime(p) and numtheory:-bigomega(rev(p)) = 2, [seq(i,i=3..1000,2)]);

s = {}; Do[If[2 == PrimeOmega[sm = FromDigits[Reverse[IntegerDigits[Prime[k]]]]], AppendTo[s, sm]], {k, 200}]; s

a(n) = A004086(A085778(n)).

cp's OEIS Frontend

A182180 Semiprimes that become prime when their digits are sorted into nonincreasing order.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Extensions

A264815 Semirps: a semirp (or semi-r-p) is a semiprime r*p with r and p both reversed primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Sage

Formula

A368238 Semiprimes whose reversal is a prime, ordered by the prime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula