A071786 -id:A071786 - cp's OEIS frontend

A341090 Fully multiplicative: for any prime p, if the reversal of p in base 10, say q, is prime, then a(p) = q, otherwise a(p) = p.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 14, 15, 16, 71, 18, 19, 20, 21, 22, 23, 24, 25, 62, 27, 28, 29, 30, 13, 32, 33, 142, 35, 36, 73, 38, 93, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 213, 124, 53, 54, 55, 56, 57, 58, 59, 60, 61, 26, 63, 64, 155, 66

Offset: 1

Rémy Sigrist, Feb 13 2022

This sequence is a self-inverse permutation of the natural numbers.

			For n = 377:
- 377 = 13 * 29,
- the reversal of 13, 31, is prime,
- the reversal of 29, 92, is not prime,
- so a(377) = 31 * 29 = 899.

Cf. A004086, A071786, A235027.

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; mul((q->
     `if`(isprime(q), q, j[1]))(R(j[1]))^j[2], j=ifactors(n)[2])
    end:
seq(a(n), n=1..66);  # Alois P. Heinz, Feb 15 2022

f[p_, e_] := If[PrimeQ[(q = IntegerReverse[p])], q, p]^e; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 15 2022 *)

a(n) = { my (f=factor(n)); prod (k=1, #f~, my (p=f[k,1], e=f[k,2], q=fromdigits(Vecrev(digits(p)))); if (isprime(q), q, p)^e) }

A257842 Semiprimes pq such that R(pq) = R(p)*R(q), where R = A004086 = reverse digits.

Original entry on oeis.org

4, 6, 9, 22, 26, 33, 39, 46, 55, 62, 69, 77, 82, 86, 93, 121, 143, 169, 187, 202, 206, 226, 253, 262, 299, 303, 309, 339, 341, 393, 422, 446, 451, 466, 473, 482, 505, 583, 622, 626, 633, 662, 669, 671, 699, 707, 781, 802, 842, 862, 866, 886, 933, 939, 961

Offset: 1

M. F. Hasler, May 11 2015

A subsequence of A161600. Almost all terms with less than 4 digits are either multiples of 2 or 3 or of 11.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A161600, A071786, A004086.

N:= 1000: # to get all terms <= N
digrev:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
F:= proc(p,q) if digrev(p*q)=digrev(p)*digrev(q) then p*q else NULL fi end proc:
sort([seq(seq(F(Primes[i],q), q = select(`<=`,Primes[i..-1],N/Primes[i])), i=1..nops(Primes))]); # Robert Israel, May 14 2015

f[n_]:=FactorInteger[n][[1,1]];g[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Select[Range@1000,PrimeOmega[#]==2&&g[f[#]*#/f[#]]==g[f[#]]*g[#/f[#]]&] (* Ivan N. Ianakiev, May 14 2015 *)

is(n)=bigomega(n)==2&&!eval(concat(Vecrev(Str(n"-"vecmin(n=factor(n)[,1])"*"vecmax(n)))))

cp's OEIS Frontend

A341090 Fully multiplicative: for any prime p, if the reversal of p in base 10, say q, is prime, then a(p) = q, otherwise a(p) = p.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A257842 Semiprimes pq such that R(pq) = R(p)*R(q), where R = A004086 = reverse digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

cp's OEIS Frontend

A341090 Fully multiplicative: for any prime p, if the reversal of p in base 10, say q, is prime, then a(p) = q, otherwise a(p) = p.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A257842 Semiprimes p*q such that R(p*q) = R(p)*R(q), where R = A004086 = reverse digits.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A257842 Semiprimes pq such that R(pq) = R(p)*R(q), where R = A004086 = reverse digits.