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 A220746 Numbers n such that n and n + 10 are prime and there is a power of two in the interval (n, n+10). 2
 3, 7, 13, 31, 61, 127, 1021, 1048573, 23945242826029513411849172299223580994042798784118781 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..9. MATHEMATICA Union[Flatten[Table[Select[Range[2^n - 9, 2^n - 1, 2], PrimeQ[#] && PrimeQ[# + 10] &], {n, 3, 200}]]] (* T. D. Noe, Feb 20 2013 *) Union[Flatten[Table[Select[Thread[{Range[2^n-10, 2^n], Range[ 2^n, 2^n+10]}], AllTrue[ #, PrimeQ]&], {n, 3, 1000}], 1][[;; , 1]]] (* Harvey P. Dale, Feb 19 2023 *) PROG (Magma) //Program finds primes separated by an even number (called gap) which //have a power of two between them. Program starts with the smallest //power of two above gap. Primes less than this starting point can be //checked by inspection. In this example 3 also works. gap:=10; start:=Ilog2(gap)+1; for i:= start to 1000 do powerof2:=2^i; for k:=powerof2-gap+1 to powerof2-1 by 2 do if (IsPrime(k) and IsPrime(k+gap)) then k; end if; end for; end for; (PARI) print1(3); for(n=4, 500, forprime(p=2^n-9, 2^n-1, if(isprime(p+10), print1(", "p)))) \\ Charles R Greathouse IV, Feb 20 2013 CROSSREFS Cf. A023203, A221211. Sequence in context: A060424 A119962 A333877 * A110436 A126879 A247895 Adjacent sequences: A220743 A220744 A220745 * A220747 A220748 A220749 KEYWORD nonn AUTHOR Brad Clardy, Feb 20 2013 STATUS approved

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Last modified November 30 21:14 EST 2023. Contains 367462 sequences. (Running on oeis4.)