A283805 k-digit composite numbers Sum_{j=0..k-1} d_(j)*10^j with exactly k prime factors, p_(0), p_(1), ..., p_(k-2), p_(k-1), written in ascending order, such that Sum_{j=0..k-1} d_(j)^p_(j) is a prime number.

14, 102, 110, 164, 212, 290, 434, 595, 1060, 1068, 1110, 1112, 1190, 1220, 1284, 1356, 1448, 1460, 1572, 1668, 1804, 1884, 1938, 2090, 2108, 2892, 3185, 3770, 3972, 5358, 9790, 10010, 10020, 10040, 10100, 10136, 10220, 10448, 10536, 10664, 10668, 10868, 10998, 11052

Offset

1,1

Links

Table of n, a(n) for n=1..44.

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

Example

14 = 2 * 7 and 4^2 + 1^7 = 17 is prime;
102 = 2 * 3 * 17 = 2^2 + 0^3 + 1^17 = 5 is prime;
110 = 2 * 5 * 11 and 0^2 + 1^5 + 1^11 = 2 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);
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[ Reverse[d]^ Flatten[#[[1]] + 0 Range@#[[2]] & /@ f]]]; Select[ Range[10^4], ok] (* Giovanni Resta, Mar 17 2017 *)

Crossrefs

Cf. A283804.

Sequence in context: A041370 A244883 A055913 * A005757 A295210 A255721

Adjacent sequences: A283802 A283803 A283804 * A283806 A283807 A283808

Keyword

nonn,base

Author

Paolo P. Lava, Mar 17 2017

Status

approved