A032360 -id:A032360 - cp's OEIS frontend

A002238 Numbers k such that 21*2^k - 1 is prime.

1, 2, 3, 7, 10, 13, 18, 27, 37, 51, 74, 157, 271, 458, 530, 891, 1723, 1793, 1849, 1986, 2191, 2869, 4993, 7777, 11730, 15313, 29171, 35899, 36227, 71570, 199219, 233914, 297499, 332523, 348547, 538657, 986130, 999599

Offset: 1

N. J. A. Sloane

H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
Kosmaj, Riesel list k<300.
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A032360, 21*2^k + 1 is prime.

is(n)=ispseudoprime(21*2^n-1) \\ Charles R Greathouse IV, May 22 2017

More terms from Hugo Pfoertner, Jun 22 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

A331539 a(n) gives the number of primes of form (2n+1)2^m + 1 where m satisfies 2^m <= 2*n+1.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 1, 2, 1, 0, 2, 1, 2, 2, 2, 0, 1, 2, 2, 4, 1, 1, 1, 0, 1, 2, 2, 1, 2, 1, 1, 3, 3, 2, 2, 2, 2, 4, 1, 1, 3, 2, 2, 2, 1, 0, 3, 3, 2, 4, 1, 0, 3, 1, 1, 2, 2, 1, 3, 2, 0, 1, 2, 1, 2, 2, 2, 4, 1, 1, 4, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 3, 5, 1, 1, 0, 1

Offset: 0

Jeppe Stig Nielsen, Jan 19 2020

nonn

For each index n, let k = 2*n+1. Then a(n) gives the number of primes of form k*2^m + 1 that are NOT considered Proth primes (A080076) because their m are too small.

In the edge case n=0, so k=1, we count 1*2^0 + 1 = 2 as a non-Proth prime.

			For n=10, we consider 21*2^m + 1, where m runs from 0 to 4 (the next value m=5 would make 2^m exceed 21). The number of cases where 21*2^m + 1 is prime, is 2, namely m=1 (prime 43) and m=4 (prime 337). So 2 primes means a(10)=2. Compare with the start of A032360, all k=21 primes.

Cf. A080076, A134876.

a[n_] := Sum[Boole @ PrimeQ[(2n+1)*2^m + 1], {m, 0, Log2[2n+1]}]; Array[a, 100, 0] (* Amiram Eldar, Jan 20 2020 *)

a(n) = my(k=2*n+1);sum(m=0,logint(k,2),ispseudoprime(k<

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A002238 Numbers k such that 21*2^k - 1 is prime.

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A331539 a(n) gives the number of primes of form (2n+1)2^m + 1 where m satisfies 2^m <= 2*n+1.

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cp's OEIS Frontend

A002238 Numbers k such that 21*2^k - 1 is prime.

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Author

Keywords

References

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Programs

PARI

Extensions

A331539 a(n) gives the number of primes of form (2*n+1)*2^m + 1 where m satisfies 2^m <= 2*n+1.

Views

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Keywords

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Mathematica

PARI

A331539 a(n) gives the number of primes of form (2n+1)2^m + 1 where m satisfies 2^m <= 2*n+1.