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.
35=5*7 is semiprime and 53 is prime.
a(3) = 89 is a term because 89 is a prime and its reversal 98 = 2*7^2 is the product of 3 primes, counted with multiplicity.
rev:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc: select(t -> isprime(t) and numtheory:-bigomega(rev(t)) = 3, [seq(i,i=3..10000,2)]);
Select[Prime[Range[350]], PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]]]==3&] (* Stefano Spezia, Nov 07 2023 *) Select[Prime[Range[400]],PrimeOmega[IntegerReverse[#]]==3&] (* Harvey P. Dale, Jan 10 2024 *)
a(3) = 47 is a term because 47 and 74/2 = 37 are primes.
revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(L[-i]*10^(i-1),i=1..nops(L)) end proc: filter:= proc(n) isprime(n) and numtheory:-bigomega(revdigs(n))=2 end proc: select(filter, [seq(seq(seq(i*10^d+j,j=1..10^d-1,2),i=2..8,2),d=1..4)]);
isok(p) = if (isprime(p), my(r=fromdigits(Vecrev(digits(p)))); if (!(r%2), isprime(r/2))); \\ Michel Marcus, Jun 15 2021
from sympy import isprime, primerange def ok(p): t = int(str(p)[::-1]); return t%2 == 0 and isprime(t//2) print(list(filter(ok, primerange(1, 2838)))) # Michael S. Branicky, Jun 16 2021
a(3) = 647 is a term because 647 is prime, its reverse 746 = 2*373 is a semiprime, 647+746 = 1393 = 7*199 is a semiprime, and the reverse 3931 of 1393 is a prime.
filter:= proc(p) local q,r,s;
if not isprime(p) then return false fi;
q:= digrev(p);
if numtheory:-bigomega(q) <> 2 then return false fi;
r:= p+q;
s:= digrev(r);
{numtheory:-bigomega(r), numtheory:-bigomega(s)} = {1,2}
end proc:
digrev:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
select(filter, [seq(i,i=3..10^5,2)]);
semiQ[n_] := PrimeOmega[n] == 2; q1[p_] := PrimeQ[p] && semiQ[IntegerReverse[p]]; q2[p_] := semiQ[p] && PrimeQ[IntegerReverse[p]]; q[p_] := q1[p] && (q1[(s = p + IntegerReverse[p])] || q2[s]); Select[Range[30000], q] (* Amiram Eldar, Jan 16 2022 *) pspQ[p_]:=With[{q=IntegerReverse[p]},PrimeOmega[q]==2&&Sort[PrimeOmega/@{p+q,IntegerReverse[p+q]}]=={1,2}]; Select[Prime[ Range[ 3500]],pspQ] (* Harvey P. Dale, Mar 22 2025 *)
from sympy import isprime, factorint
def issemip(n): return sum(factorint(n).values()) == 2
def ok(p):
if not isprime(p): return False
q = int(str(p)[::-1])
if not issemip(q): return False
r = int(str(p+q)[::-1])
return (isprime(p+q) and issemip(r)) or (isprime(r) and issemip(p+q))
print([k for k in range(30000) if ok(k)]) # Michael S. Branicky, Jan 15 2022
a(4) = 74 because A115670(4) = 47 is the 4th prime whose reversal is a semiprime, and 74 is that reversal.
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