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

0,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A156759, A247393, A247394.

Sequence in context: A350507 A007021 A100605 * A183947 A154322 A090031

Adjacent sequences: A247392 A247393 A247394 * A247396 A247397 A247398

Keyword

nonn,easy,changed

Author

Vladimir Shevelev, Sep 16 2014

Extensions

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

Status

approved