A334101 -id:A334101 - cp's OEIS frontend

A335911 Numbers of the form q*(2^k), where k >= 0 and q is either a Fermat prime or a Mersenne prime; Numbers k for which A335885(k) = 1.

3, 5, 6, 7, 10, 12, 14, 17, 20, 24, 28, 31, 34, 40, 48, 56, 62, 68, 80, 96, 112, 124, 127, 136, 160, 192, 224, 248, 254, 257, 272, 320, 384, 448, 496, 508, 514, 544, 640, 768, 896, 992, 1016, 1028, 1088, 1280, 1536, 1792, 1984, 2032, 2056, 2176, 2560, 3072, 3584, 3968, 4064, 4112, 4352, 5120, 6144, 7168, 7936, 8128, 8191

Offset: 1

Antti Karttunen, Jun 30 2020

nonn

Numbers k such that A000265(k) is either in A000668 or in A019434.

Product of any two terms (whether distinct or not) can be found in A335912.

Row 1 of A335910.
Union of A334101 and A335431. Subsequence of A038550.
Cf. A000668, A000668, A335885, A335912.
Cf. A141453 (after its initial 2, gives the primes present in this sequence).

A335885(n) = { my(f=factor(n)); sum(k=1,#f~,if(2==f[k,1],0,f[k,2]*(1+min(A335885(f[k,1]-1),A335885(f[k,1]+1))))); };
isA335911(n) = (1==A335885(n));

A000265(n) = (n>>valuation(n,2));
isA000668(n) = (isprime(n)&&!bitand(n,1+n));
isA019434(n) = ((n>2)&&isprime(n)&&!bitand(n-2, n-1));
isA335911(n) = (isA000668(A000265(n))||isA019434(A000265(n)));

A359584 Positions of odd terms in A329697.

Original entry on oeis.org

3, 5, 6, 10, 12, 17, 19, 20, 21, 23, 24, 27, 29, 31, 33, 34, 35, 37, 38, 39, 40, 42, 45, 46, 48, 53, 54, 55, 58, 61, 62, 65, 66, 68, 70, 73, 74, 75, 76, 78, 80, 83, 84, 89, 90, 92, 96, 101, 103, 106, 108, 110, 113, 116, 119, 122, 123, 124, 125, 127, 129, 130, 132, 133, 136, 139, 140, 141, 146, 147

Offset: 1

Antti Karttunen, Jan 07 2023

nonn

Numbers that occur on odd-indexed rows of array A334100.

Positions of -1's in A359581, positions of 1's in A359583 (characteristic function).
Cf. A329697, A334100, A359585 (complement).
Cf. A334101, A334103, A334105 (subsequences).

PARI
```
isA359584(n) = A359583(n);
```

A350069 Semiprimes k such that 1+(2^(1+A243055(k))) is a Fermat prime, where A243055(k) gives the difference between the indices of the smallest and the largest prime divisor of k.

Original entry on oeis.org

4, 6, 9, 14, 15, 25, 33, 35, 38, 49, 65, 69, 77, 106, 119, 121, 143, 145, 169, 177, 209, 217, 221, 289, 299, 305, 323, 361, 407, 437, 469, 493, 529, 533, 589, 667, 731, 781, 841, 851, 893, 899, 949, 961, 1147, 1189, 1219, 1333, 1343, 1369, 1517, 1577, 1681, 1711, 1739, 1763, 1849, 1891, 2021, 2047, 2173, 2209, 2479

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

			9 is a semiprime (9 = 3*3), and as the difference between the indices of the smallest (3) and the largest prime (3) dividing 9 is 0, we have 1+(2^(1+A243055(k))) = 3, which is in A019434, and therefore 9 is included in this sequence, like all squares of primes (A001248).
177 = 3 * 59 = prime(2) * prime(17), therefore A243055(177) = 17-2 = 15, and as 1+(2^16) = 65537 is also in A019434, 177 is included in this sequence.

Index entries for sequences computed from indices in prime factorization

Positions of ones in A342651.
Cf. A019434, A209229, A243055, A334101.
Subsequence of A001358. A001248 is a subsequence.

A209229(n) = (n && !bitand(n,n-1));
A243055(n) = if(1==n,0,my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); (primepi(gpf)-primepi(lpf)));
isA350069(n) = if(2!=bigomega(n),0,my(d=1+A243055(n)); (A209229(d) && isprime(1+(2^d))));

cp's OEIS Frontend

A335911 Numbers of the form q*(2^k), where k >= 0 and q is either a Fermat prime or a Mersenne prime; Numbers k for which A335885(k) = 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

PARI

A359584 Positions of odd terms in A329697.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A350069 Semiprimes k such that 1+(2^(1+A243055(k))) is a Fermat prime, where A243055(k) gives the difference between the indices of the smallest and the largest prime divisor of k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI