A101324 Primes p such that p+1=C(q)=q-th composite and q is prime.

7, 13, 19, 29, 43, 53, 61, 107, 113, 181, 193, 229, 251, 317, 337, 383, 433, 463, 491, 601, 827, 857, 887, 997, 1033, 1061, 1163, 1193, 1307, 1373, 1531, 1693, 1699, 1721, 1789, 1811, 1831, 1931, 2003, 2029, 2267, 2339, 2347

Offset: 1

Author

Robin Garcia, Dec 24 2004

Keywords

• nonn

Comments

In general P(k)=k-th prime=k+n where n is the index of the composite P(k)+1 (k>=2)

Examples

			a(5)=43 because 43+1=44=C(29) and 29 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A100718.

Programs

Mathematica

Module[{nn=3000,cmps,pcmps,c},cmps=Select[Range[nn],CompositeQ];pcmps=Thread[{Range[Length[cmps]],cmps}];c=Select[pcmps,PrimeQ[ #[[1]]]&][[;;,2]]; Select[ Prime[ Range[ nn]],MemberQ[c,#+1]&]]//Rest (* Harvey P. Dale, Mar 17 2025 *)