A352581 Numbers k such that A001414(k+1) = A001414(k)+1 and A001414(k)^2+3*A001414(k)+1 is prime.

2, 3, 4, 20, 24, 1104, 1274, 2079, 4345, 13775, 14905, 20220, 23408, 25592, 35167, 49230, 61456, 66585, 68479, 75648, 76640, 121539, 172255, 194403, 200384, 229581, 233090, 236282, 238017, 247475, 263145, 283590, 287615, 295274, 295640, 326451, 386169, 422065, 429385, 429802, 475968, 585310

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 21 2022

Keywords

• nonn

Comments

Numbers k such that A001414(k+1) = A001414(k)+1 and (A001414(k)+1)*(A001414(k+1)+1)-1 is prime.

Examples

			a(4) = 20 is a term because A001414(20) = 9, A001414(21) = 10 = 9+1, and 10*11-1 = 109 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A228126 and A352580. Cf. A001414.

Programs

Maple

spf:= proc(n) local t; option remember; add(t[1]*t[2], t=ifactors(n)[2]) end proc:
select(t -> (spf(t+1) = spf(t)+1) and isprime(spf(t)^2 + 3*spf(t)+1), [$1..10^6]);