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 A243145 Least positive number k such that n+k and n+k^2 are both prime. 3
 1, 1, 2, 1, 6, 1, 4, 3, 2, 1, 6, 1, 4, 3, 2, 1, 6, 1, 12, 3, 16, 1, 6, 7, 4, 15, 2, 1, 12, 1, 6, 9, 8, 3, 6, 1, 4, 3, 2, 1, 30, 1, 4, 3, 8, 1, 6, 5, 10, 3, 10, 1, 6, 5, 4, 15, 2, 1, 42, 1, 6, 21, 4, 3, 6, 1, 4, 15, 2, 1, 30, 1, 6, 33, 8, 25, 6, 1, 10, 3, 16, 1, 24, 5, 4, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n > 1, a(n) == n+1 (mod 2). a(n) = 1 for n in A006093. - Robert Israel, Feb 02 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 8+1 and 8+1^2 (9) isn't prime. 8+2 and 8+2^2 (10 and 12) aren't both prime. But 8+3 and 8+3^2 (11 and 17) are both prime. Thus a(8) = 3. MAPLE f:= proc(n) local k;   for k from (n mod 2)+1 by 2 do     if isprime(n+k) and isprime(n+k^2) then return k fi   od end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Feb 02 2018 MATHEMATICA f[n_] := Module[{k}, For[k = Mod[n, 2] + 1, True, k += 2, If[PrimeQ[n + k] && PrimeQ[n + k^2], Return[k]]]]; f[1] = 1; f /@ Range[100] (* Jean-François Alcover, Feb 03 2018, after Robert Israel *) PROG (PARI) a(n)=for(k=1, 10^6, if(ispseudoprime(n+k)&&ispseudoprime(n+k^2), return(k))) n=1; while(n<100, print1(a(n), ", "); n+=1) (Python) from sympy import isprime, nextprime def A243145(n):     m = n     while True:         m = nextprime(m)         k = m-n         if isprime(n+k**2):             return k #  Chai Wah Wu, Sep 03 2019 CROSSREFS Cf. A006093. Sequence in context: A321725 A154744 A285038 * A306695 A242926 A189733 Adjacent sequences:  A243142 A243143 A243144 * A243146 A243147 A243148 KEYWORD nonn AUTHOR Derek Orr, May 30 2014 STATUS approved

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Last modified January 21 16:54 EST 2020. Contains 331114 sequences. (Running on oeis4.)