A072185 Primes p = x1x2x3...xn in base 10 such that x1^p1 + x2^p2 + x3^p3 + ... + xn^pn is a prime, where pn is the n-th prime.

11, 23, 29, 41, 43, 47, 61, 67, 101, 131, 139, 151, 173, 179, 199, 263, 311, 331, 337, 359, 401, 461, 593, 601, 607, 641, 757, 809, 821, 827, 863, 881, 887, 911, 953, 977, 991, 1019, 1091, 1097, 1109, 1123, 1181, 1217, 1301, 1321, 1381, 1451, 1499, 1583

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

23 belongs to the sequence because 2^2 + 3^3 = 31 is a prime.

Maple

From R. J. Mathar, Oct 10 2010: (Start)
isA072185 := proc(n) local d ; if isprime(n) then d := convert(n, base, 10) ; sdg := add( op(-i, d)^ithprime(i), i=1..nops(d)) ; isprime(sdg) ; else false; end if; end proc:
for p from 2 to 2000 do if isA072185(p) then printf("%d, ", p) ; fi; end do: (End)

Prog

(UBASIC) 30 for I=10 to 100000 40 L=alen(I) 50 Q=2:A=0 60 A1=val(mid(str(I), 2, 1)) 70 for H=2 to L 80 A=A+val(mid(str(I), H+1, 1))^nxtprm(Q) 90 Q=nxtprm(Q) 100 next 110 P=A+A1^2 120 if prmdiv(P)=P and P<>1 and prmdiv(I)=I and I<>1 then print I 130 next

Crossrefs

Sequence in context: A164932 A086244 A091939 * A105898 A247228 A243461

Adjacent sequences: A072182 A072183 A072184 * A072186 A072187 A072188

Keyword

easy,base,nonn

Author

Felice Russo, Jul 01 2002

Extensions

More terms from R. J. Mathar, Oct 10 2010

Status

approved