A127356 a(n) is the smallest k > 0 such that k^2 + prime(n) is prime.
1, 2, 6, 2, 6, 2, 6, 2, 6, 12, 4, 2, 24, 2, 6, 6, 18, 6, 2, 6, 4, 2, 12, 12, 2, 6, 2, 12, 2, 6, 2, 6, 6, 10, 12, 4, 4, 2, 12, 12, 18, 4, 6, 2, 6, 8, 4, 2, 6, 2, 6, 12, 4, 24, 6, 18, 18, 6, 2, 6, 8, 18, 2, 6, 2, 6, 4, 4, 6, 2, 6, 12, 4, 4, 2, 6, 30, 2, 24, 10
Offset: 1
Keywords
Examples
17 = prime(7); 17 + 1^2 = 18, 17 + 2^2 = 21, 17 + 3^2 = 26, 17 + 4^2 = 33, 17 + 5^2 = 42 are all composite, but 17 + 6^2 = 53 is prime. Hence a(7) = 6.
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000
Programs
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Maple
a:=proc(n) local A,j: A:={}: for j from 1 to 50 do if isprime(ithprime(n)+j^2)=true then A:=A union {j} else A:=A fi od: A[1]: end: seq(a(n),n=1..120); # Emeric Deutsch, Apr 01 2007 A127356 := proc(n) local p,a; p := ithprime(n) ; a := 1 ; while not isprime(p+a^2) do a := a+1 ; od ; RETURN(a) ; end: for n from 1 to 120 do printf("%d,",A127356(n)) ; od ; # R. J. Mathar, Apr 02 2007
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Mathematica
Join[{1},Table[p=Prime[n];x=2;While[!PrimeQ[a=p+x^2],x=x+2]; x,{n,2,100}]] (* Zak Seidov, Oct 12 2012 *) sk[n_]:=Module[{k=2},While[!PrimeQ[n+k^2],k=k+2];k]; Join[{1},Table[sk[n],{n,Prime[Range[2,80]]}]] (* Harvey P. Dale, Jul 26 2017 *)
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PARI
{for(n=1, 93, p=prime(n); k=1; while(!isprime(p+k^2), k++); print1(k, ","))} /* Klaus Brockhaus, Apr 05 2007 */
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Python
from sympy import isprime, nextprime, prime def a(n): if n == 1: return 1 k, pn = 2, prime(n) while not isprime(pn + k*k): k += 2 return k print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Nov 11 2022
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