A260350 -id:A260350 - cp's OEIS frontend

A067760 a(n) is the least positive k such that (2n+1) + 2^k is prime, or 0 if no such k exists.

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 4, 2, 1, 2, 1, 1, 2, 1, 5, 2, 1, 3, 2, 1, 1, 8, 2, 1, 2, 1, 1, 4, 2, 1, 2, 1, 7, 2, 1, 3, 4, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 7, 4, 5, 3, 4, 2, 1, 2, 1, 3, 2, 1, 1, 10, 3, 3, 2, 1, 1, 4, 2, 1, 4, 2, 1, 2, 1, 5, 2, 1, 3, 2, 1, 1, 4, 3, 3, 2, 1, 1, 2, 1, 1, 6, 5, 3, 6

Offset: 0

Don Reble, Feb 05 2002

nonn

From Phil Moore (moorep(AT)lanecc.edu), Dec 14 2009: (Start)
It is known that a(39278) = 0, since no such prime exists for the Sierpiński number 78557 (cf. A076336).
It has recently been discovered that 2131+2^4583176 and 41693+2^5146295 are probable primes, so a(1065) is probably 4583176 and a(20846) is probably 5146295.
At present, the only odd value less than 78557 for which no prime or strong probable prime of the form t+2^k is known is t = 40291, so a(20145) is completely unknown. In addition, for 25 values of t < 78557, only strong probable primes are known. (End)
The last case was resolved in 2011 when the probable prime 40291+2^9092392 was found as a part of a distributed project "Five or Bust". See links. - Jeppe Stig Nielsen, Mar 29 2019

			a(15)=4 because (2*15+1)+2^k is composite for k=1,2,3 and prime for k=4.

Jinyuan Wang, Table of n, a(n) for n = 0..39278 (terms 0..1064 from T. D. Noe, terms 1065..3000 from Richard N. Smith).
Mersenne Forum, Five or Bust
Carlos Rivera, Puzzle 167. Primes m + 2^j & m - 2^j, The Prime Puzzles and Problems Connection.

Cf. A016014, A050412, A066081, A033919, A094076, A076336, A260350, A263874, A263875 (records).

a(n) = {my(k=1); while (! isprime((2*n+1)+2^k), k++); k;} \\ Michel Marcus, Feb 26 2018

A361999 a(n) is the smallest k such that A361902(k) = n, or -1 if no such k exists.

Original entry on oeis.org

2, 1, -1, 0, 8, 24, 33, 90, 116, 25, 402, 140, 85, 120, 692, 91, 472, 1240, 369, 762, 694, 551, 3290, 322, 121, 2758, 1164, 321, 778, 3144, 663, 3418, 4684, 721, 8590, 3222, 511, 7424, 5202, 391, 3364, 10392, 531, 9710, 1714, 891, 27116, 11008, 703, 19132, 8898

Offset: 0

Pontus von Brömssen, Apr 02 2023

sign

Pontus von Brömssen, Table of n, a(n) for n = 0..500

Cf. A260350, A361902.

A260349 a(n) = min(k : A046067((k+1)/2) = n).

Original entry on oeis.org

1, 3, 7, 17, 55, 59, 19, 167, 31, 311, 289, 227, 351, 203, 379, 197, 103, 1253, 829, 335, 211, 353, 649, 437, 1921, 1853, 2869, 917, 361, 263, 283, 1637, 1213, 3353, 1519, 797, 241, 1691, 259, 1391, 2503, 1109, 3859, 1857

Offset: 0

Hugo van der Sanden, Jul 23 2015

nonn

a(n) is the first odd number k for which k * 2^i + 1 is prime when i = n but composite for all i: 0 <= i < n, or 0 if no such k exists. Thus it is the first k for which A046067((k+1)/2) = n, and therefore also the first k for which you need to test the primality of exactly n values to show that it is not a Sierpiński number.

Jaeschke shows that for each n>0, the set {k : A046067((k+1)/2) = n} is infinite. - Jeppe Stig Nielsen, Jul 06 2020

			7 * 2^i + 1 is composite for i < 2 (with values 8, 15) but prime for i = 2 (29); the smaller odd numbers 1, 3 and 5 each yield a prime for smaller i, so a(2) = 7.

Hugo van der Sanden, Table of n, a(n) for n = 0..3253
G. Jaeschke, On the Smallest k Such that All k*2^N + 1 are Composite, Mathematics of Computation, Vol. 40, No. 161 (Jan., 1983), pp. 381-384.

Cf. A046067, A076336, A260350.

a(n)=forstep(k=1,+oo,2,for(i=0,n-1,ispseudoprime(k<Jeppe Stig Nielsen, Jul 06 2020

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A067760 a(n) is the least positive k such that (2n+1) + 2^k is prime, or 0 if no such k exists.

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A361999 a(n) is the smallest k such that A361902(k) = n, or -1 if no such k exists.

Views

Author

Keywords

Links

Crossrefs

A260349 a(n) = min(k : A046067((k+1)/2) = n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI