A381532 Smallest integer k>0 such that prime(n) + k*prime(n+1) is prime.
1, 2, 2, 2, 2, 2, 6, 6, 4, 8, 4, 6, 2, 2, 10, 10, 2, 6, 12, 6, 4, 6, 4, 2, 14, 2, 2, 6, 6, 2, 2, 6, 6, 6, 20, 6, 4, 8, 4, 16, 2, 2, 2, 2, 8, 10, 4, 2, 6, 6, 6, 14, 2, 4, 10, 6, 2, 6, 2, 6, 18, 2, 2, 2, 2, 12, 10, 2, 6, 6, 4, 2, 22, 4, 6, 10, 12, 6, 8, 8, 12, 2
Offset: 1
Keywords
Examples
a(1)= 1, because 2 and 3 are consecutive primes and 2 + 1*3 = 5 is prime, and no lesser number has this property. p + k*q, where p and q are consecutive primes 2 + 1* 3 = 5 is prime; 3 + 2* 5 = 13 is prime; 5 + 2* 7 = 19 is prime; 7 + 2*11 = 29 is prime;
Crossrefs
Programs
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Mathematica
Do[k=0;Until[PrimeQ[Prime[n]+k*Prime[n+1]],k++];a[n]=k,{n,82}];Array[a,82] (* James C. McMahon, Mar 28 2025 *) -
PARI
a(n) = my(p=prime(n), q=nextprime(p+1), k=1); while (!isprime(p+k*q), k++); k; \\ Michel Marcus, Mar 09 2025