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

Author

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

Keywords

• nonn
• base
• fini
• full

Comments

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".

Examples

			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).
		

Crossrefs

Cf. A000040, A033548, A134966, A177061.

Programs

Maple

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

Extensions

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