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

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Last modified September 18 11:08 EDT 2024. Contains 375999 sequences. (Running on oeis4.)