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A214120 Number of Proth primes < 2^n. 1
0, 1, 2, 3, 4, 5, 7, 9, 12, 17, 21, 27, 33, 50, 62, 84, 110, 148, 182, 253, 327, 467, 610, 855, 1097, 1548, 1999, 2849, 3648, 5231, 6761, 9781, 12631, 18293, 23770, 34407, 44704, 64911, 84734, 122742, 160055, 233124, 303882, 442949, 578588, 843890, 1103500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..47.

Chris Caldwell, The Top 20 Proth Primes

Chris Caldwell, The Prime Glossary, Proth prime

EXAMPLE

a(5) = 4 since first 4 Proth primes are 3, 5, 13, 17 all < 2^5.

MATHEMATICA

lst2 = {}; r = 47; lst1 = Union[Flatten@Table[Select[1 + 2^k*Range[1, 2^Min[k, r - k], 2], # < 2^r && PrimeQ[#] &], {k, r}]]; Do[AppendTo[lst2, Length@Select[lst1, # < 2^n &]], {n, r}]; lst2

PROG

(PARI) a(n)=my(c=0); for(m=1, n-1, k=1; until(k>2^m, p=k*2^m+1; if(p>2^n, break); if(isprime(p), c++); k=k+2)); c; \\ Arkadiusz Wesolowski, Mar 14 2014

CROSSREFS

Cf. A080076.

Sequence in context: A112639 A290137 A241818 * A240840 A117599 A117602

Adjacent sequences:  A214117 A214118 A214119 * A214121 A214122 A214123

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Jul 04 2012

STATUS

approved

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Last modified November 22 03:43 EST 2019. Contains 329388 sequences. (Running on oeis4.)