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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)