A177275 - OEIS

%I #5 Jul 04 2013 11:39:20

%S 112573,115237,115327,211573,235117,257311,327511,352711,357211,

%T 372511,511237,511327,511723,521137,521173,572311,711523,725113,

%U 735211,751123

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

%C There are 20 terms in the sequence. Each is a 6-digit prime with sum of digits equal to 19 = A051351(5).

%C 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)):

%C (10668,21), (10892,20), (10901,11), (18940,22), (20845,19) HP,

%C (22622,14), (28208,20), (30192,15), (30538,19) HP, (31709,20),

%C (42386,23), (42392,20), (42426,18), (43145,17), (43149,21),

%C (47000,11), (57421,19) HP, (58426,25), (59175,27), (60315,15)

%C Where prime(i) is in A033548, this is marked as "HP" for "Honaker Prime".

%e a(1) = 11//2//5//7//3 = 112573 = prime(10668).

%e a(5) = 2//3//5//11//7 = 235117 = prime(20845).

%e a(20) = 7//5//11//2//3 = 751123 = prime(60315).

%p 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:

%p 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:

%p A177275() ; # _R. J. Mathar_, May 09 2010

%Y Cf. A000040, A033548, A134966, A177061.

%K nonn,base,fini,full

%O 1,1

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

%E Added keyword:base,full. Removed the variable p. - _R. J. Mathar_ and _Zak Seidov_, May 09 2010