A247395 The smallest numbers of every class in a classification of positive numbers (see comment).

1, 2, 4, 10, 26, 50, 122, 170, 290, 362, 530, 842, 962, 1370, 1682, 1850, 2210, 2810, 3482, 3722, 4490, 5042, 5330, 6242, 6890, 7922, 9410, 10202, 10610, 11450, 11882, 12770, 16130, 17162, 18770, 19322, 22202, 22802, 24650, 26570, 27890, 29930, 32042, 32762

Offset: 0

Author

Vladimir Shevelev, Sep 16 2014

Keywords

• nonn
• easy

Comments

Consider a classification of the positive numbers with classes {1}, A000040 (primes), A156759 (n>=2) (preprimes, or preprimes of the first kind), A247393 (preprimes of the second kind), A247394 (preprimes of the third kind), etc.

Then a(0)=1, a(1)=2; for n>=3, a(n) is the smallest number which is a preprime of the (n-1)st kind.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..1000
• Vladimir Shevelev, A classification of the positive integers over primes

Crossrefs

Cf. A000040, A156759, A247393, A247394.

Programs

Mathematica

Table[If[n>2, Prime[n - 1]^2 + 1, 2^n], {n, 0, 43}] (* Indranil Ghosh, Mar 08 2017 *)

PARI

a(n)=if(n>2, (prime(n-1))^2 + 1, 2^n) \\ Charles R Greathouse IV, Sep 17 2014

Formula

For n>=3, a(n) = (prime(n-1))^2 + 1.

Extensions

More terms from Peter J. C. Moses, Sep 16 2014