A177061 -id:A177061 - cp's OEIS frontend

A177275 Primes which are a concatenation of some permutation of the first 5 primes.

112573, 115237, 115327, 211573, 235117, 257311, 327511, 352711, 357211, 372511, 511237, 511327, 511723, 521137, 521173, 572311, 711523, 725113, 735211, 751123

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 06 2010

There are 20 terms in the sequence. Each is a 6-digit prime with sum of digits equal to 19 = A051351(5).
For each of the 20 entries we define the index i via prime(i) = a(n), which yields the following 20 pairs of (i, A007953(i)):
(10668,21), (10892,20), (10901,11), (18940,22), (20845,19) HP,
(22622,14), (28208,20), (30192,15), (30538,19) HP, (31709,20),
(42386,23), (42392,20), (42426,18), (43145,17), (43149,21),
(47000,11), (57421,19) HP, (58426,25), (59175,27), (60315,15)
Where prime(i) is in A033548, this is marked as "HP" for "Honaker Prime".

			a(1) = 11//2//5//7//3 = 112573 = prime(10668).
a(5) = 2//3//5//11//7 = 235117 = prime(20845).
a(20) = 7//5//11//2//3 = 751123 = prime(60315).

Cf. A000040, A033548, A134966, A177061.

catL := proc(L) local a,i,dgs ; a := op(1,L) ; for i from 2 to nops(L) do dgs := max(1, 1+ilog10(op(i,L))) ; a := a*10^dgs+op(i,L) ; end do: a ; end proc:
A177275 := proc() local pL,a,c ; pL := [seq(ithprime(c),c=1..5)] ; a := {} ; for c in combinat[permute](pL) do p := catL(c) ; if isprime(p) then a := a union {p} ; end if; end do: print(sort(a)) ; end proc:
A177275() ; # R. J. Mathar, May 09 2010

Added keyword:base,full. Removed the variable p. - R. J. Mathar and Zak Seidov, May 09 2010

A347612 Semiprimes formed from single-digits primes only, each used at most once.

Original entry on oeis.org

25, 35, 57, 235, 237, 253, 327, 527, 537, 573, 723, 753, 2537, 2573, 2735, 5327, 5723, 7235

Offset: 1

Harvey P. Dale, Sep 08 2021

			527 is a semiprime and its non-repeating digits are primes.

Cf. A177061, A000040, A168349, A168385.

Select[FromDigits/@Flatten[Permutations/@Subsets[ {2,3,5,7}],1],PrimeOmega[ #] == 2&]//Union

A362678 Primes whose digits are prime and in nondecreasing order.

Original entry on oeis.org

2, 3, 5, 7, 23, 37, 223, 227, 233, 257, 277, 337, 557, 577, 2237, 2333, 2357, 2377, 2557, 2777, 3557, 5557, 22277, 22777, 23333, 23357, 23557, 25577, 33377, 33577, 222337, 222557, 223337, 223577, 233357, 233557, 233777, 235577, 333337, 335557, 355777

Offset: 1

James C. McMahon, Jul 03 2023

Intersection of A009994 and A019546.

The subsequence for primes whose digits are prime and in strictly increasing order has just eight terms: 2 3 5 7 23 37 257 2357 (see A177061).

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A009994, A019546, A177061.

M:= 7: # for terms with <+ M digits
R:= NULL:
for d from 1 to M do
  S:= NULL:
  for x2 from 0 to d do
    for x3 from 0 to d-x2 do
      for x5 from 0 to d-x2-x3 do
        x7:= d-x2-x3-x5;
        x:= parse(cat(2$x2,3$x3,5$x5,7$x7));
        if isprime(x) then S:= S,x fi;
    od od od;
    R:= R, op(sort([S]));
od:
R;  # Robert Israel, Jul 04 2023

Select[Prime[Range[31000]], AllTrue[d = IntegerDigits[#], PrimeQ] && LessEqual @@ d &] (* Amiram Eldar, Jul 07 2023 *)

isok(p) = if (isprime(p), my(d=digits(p)); (d == vecsort(d)) && (#select(isprime, d) == #d)); \\ Michel Marcus, Jul 07 2023

from sympy import isprime
from itertools import count, combinations_with_replacement as cwr, islice
def agen(): yield from (filter(isprime, (int("".join(c)) for d in count(1) for c in cwr("2357",d))))
print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 05 2023

A364831 Primes whose digits are prime and in nonincreasing order.

Original entry on oeis.org

2, 3, 5, 7, 53, 73, 733, 773, 5333, 7333, 7753, 55333, 75533, 75553, 77773, 733333, 755333, 775553, 7553333, 7555333, 7775533, 7777753, 55555333, 55555553, 77755553, 555553333, 755555533, 773333333, 777555553, 777773333, 777775333, 777775553, 777777773

Offset: 1

James C. McMahon, Aug 09 2023

Intersection of A028867 and A019546.

The subsequence for primes whose digits are prime and in strictly decreasing order has just six terms: 2 3 5 7 53 73 (see A177061).

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A009996, A019546, A177061, A028867.

Select[Prime[Range[3100000]], AllTrue[d = IntegerDigits[#], PrimeQ] && GreaterEqual @@ d &]

from itertools import count, islice, chain, combinations_with_replacement
from sympy import isprime
def A364831_gen(): # generator of terms
    yield 2
    yield from chain.from_iterable((sorted(s for d in combinations_with_replacement('753',l) if isprime(s:=int(''.join(d)))) for l in count(1)))
A364831_list = list(islice(A364831_gen(),30)) # Chai Wah Wu, Sep 10 2023

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A177275 Primes which are a concatenation of some permutation of the first 5 primes.

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A347612 Semiprimes formed from single-digits primes only, each used at most once.

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A362678 Primes whose digits are prime and in nondecreasing order.

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A364831 Primes whose digits are prime and in nonincreasing order.

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