A081942 a(1) = 1, a(n) = smallest number greater than a(n-1) such that a(n-1)*a(n) + 1 is prime.

1, 2, 3, 4, 7, 10, 13, 24, 25, 28, 34, 37, 40, 43, 46, 51, 56, 60, 67, 70, 79, 84, 87, 94, 105, 106, 120, 126, 130, 133, 136, 147, 148, 151, 156, 161, 162, 163, 166, 171, 176, 177, 184, 190, 193, 204, 208, 211, 228, 234, 239, 242, 248, 252, 256, 262, 265, 270

Offset: 1

Author

Amarnath Murthy, Apr 02 2003

Keywords

• nonn

Comments

See A073666 for a nonincreasing version and A096100 for a more restrictive constraint. - M. F. Hasler, Nov 24 2015

Links

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

Crossrefs

Cf. A081943, A073666, A096100.

Programs

Mathematica

f[s_List] := Block[{k = m = s[[-1]]}, k++; While[ !PrimeQ[k*m + 1], k++]; Append[s, k]]; Nest[f, {1}, 57] (* Robert G. Wilson v, Dec 02 2012 *)
smp[n_]:=Module[{m=n+1},While[!PrimeQ[m*n+1],m++];m]; NestList[smp,1,60] (* Harvey P. Dale, Dec 12 2018 *)

PARI

A081942(n,show=0,a=1)={for(n=2,n,show&&print1(a",");for(k=a+1,9e9, isprime(a*k+1) && (a=k) && break));a} \\ Use 2nd or 3rd optional arg to print intermediate terms or to use another starting value. - M. F. Hasler, Nov 24 2015

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 08 2003