A283804 k-digits composite numbers Sum_{j=0..k-1} d_(j)*10^j with exactly k prime factors, p_(k-1), p_(k-2), ..., p_(1), p_(0), written in descending order, such that Sum_{j=0..k-1} d_(j)^p_(k-j-1) is a prime number.

38, 110, 175, 212, 245, 290, 410, 434, 470, 539, 595, 610, 670, 830, 890, 902, 962, 1110, 1190, 1220, 1460, 1972, 2010, 2090, 2166, 2210, 2670, 2812, 3020, 3185, 3260, 4030, 4270, 4690, 4780, 5420, 5525, 5790, 6140, 6290, 6340, 6740, 6890, 7310, 7460, 7532, 7550

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Carlos Rivera, Puzzle 25. Composed primes (by G.L. Honaker, Jr.), The Prime Puzzles and Problems Connection.

Example

38 = 19 * 2 and 8^19 + 3^2 = 144115188075855881 is prime;
110 = 11 * 5 * 2 and 0^11 + 1^5 + 1^2 = 2 is prime;
175 = 7 * 5 * 5 and 5^7 + 7^5 + 1^5 = 94933 is prime.

Maple

with(numtheory): P:=proc(q) local a, b, c, d, j, k; global n; a:=0; k:=0;
for n from 12 to q do a:=ifactors(n)[2]; if ilog10(n)+1=bigomega(n) then d:=[];
for k from 1 to nops(a) do for j from 1 to a[k][2] do d:=[op(d), a[k][1]]; od; od; d:=sort(d);
for k from 1 to trunc(nops(d)/2) do b:=d[k]; d[k]:=d[nops(d)-k+1]; d[nops(d)-k+1]:=b; od;
b:=n; c:=0; for k from 1 to ilog10(n)+1 do c:=c+(b mod 10)^d[k]; b:=trunc(b/10); od;
if isprime(c) then print(n); fi; fi; od; end: P(10^5);

Mathematica

ok[n_] := Block[{f = FactorInteger@n, d = IntegerDigits@ n}, Total[ Last /@ f] == Length@d && PrimeQ@ Total[ d^Flatten[#[[1]] + 0 Range@#[[2]] & /@ f]]]; Select[ Range@ 7550, ok] (* Giovanni Resta, Mar 17 2017 *)

Crossrefs

Cf. A283805.

Sequence in context: A044606 A244177 A251236 * A251229 A282850 A173309

Adjacent sequences: A283801 A283802 A283803 * A283805 A283806 A283807

Keyword

nonn,base

Author

Paolo P. Lava, Mar 17 2017

Status

approved