A096915 Smallest prime which when appended to n produces a prime.
3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 7, 23, 7, 3, 3, 11, 3, 11, 11, 3, 3, 11, 7, 3, 7, 3, 3, 7, 3, 17, 7, 7, 3, 7, 3, 3, 7, 13, 11, 11, 3, 3, 7, 3, 23, 7, 19, 3, 13, 3, 23, 7, 7, 3, 7, 7, 3, 7, 3, 11, 11, 3, 3, 19, 3, 3, 11, 13, 29, 7, 3, 3, 7, 43, 3, 7, 7, 11, 11, 3, 11, 19, 3, 3, 7, 3, 23, 7, 37, 41
Offset: 1
Examples
a(20)=11 because 11 is prime and 2011 is the smallest prime starting with 20 (2003 is not allowed).
Links
- T. D. Noe, Table of n, a(n) for n=1..10000
Programs
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Mathematica
f[n_] := Block[{p = 2, a = IntegerDigits[n]}, While[ !PrimeQ[ FromDigits[ Join[a, IntegerDigits[ Prime[p]]] ]], p++ ]; Prime[p]]; Table[ f[n], {n, 92}] (* Robert G. Wilson v, Aug 20 2004 *) sp[n_]:=Module[{p=3},While[CompositeQ[n*10^IntegerLength[p]+p],p= NextPrime[ p]];p]; Array[sp,100] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 26 2019 *) -
PARI
A096915(n) = { local(p=1); until(isprime(eval(Str(n,p=nextprime(p+2)))),);p} \\ M. F. Hasler, Jan 05 2009
Extensions
More terms from Robert G. Wilson v, Aug 20 2004
Cross-reference to indices of records corrected by M. F. Hasler, Jan 14 2009