Frederic Isenmann - cp's OEIS frontend

User: Frederic Isenmann

Frederic Isenmann has authored 2 sequences.

A282329 Start with 2, then successively subtract the primes 3, 5, 7, ...

2, -1, -6, -13, -24, -37, -54, -73, -96, -125, -156, -193, -234, -277, -324, -377, -436, -497, -564, -635, -708, -787, -870, -959, -1056, -1157, -1260, -1367, -1476, -1589, -1716, -1847, -1984, -2123, -2272, -2423, -2580, -2743, -2910

Offset: 1

Frederic Isenmann, Feb 12 2017

sign

			a(1) = 2 - 3 = -1;
a(2) = 2 - 3 - 5 = -6.

Cf. A007504, A071148, A000040.

FoldList[#1 - #2 &, 2, Prime@ Range[2, 39]] (* Michael De Vlieger, Feb 12 2017 *)

lista(nn) = {s = prime(1); print1(s, ", "); for (n=2, nn, s -= prime(n); print1(s, ", "););} \\ Michel Marcus, Feb 12 2017

from sympy import prime, isprime
sub=2
print(sub, end=", ")
for i in range (3, 200, 2):
    if (isprime(i)==True):
        sub=sub-i
        print(sub, end=", ")

a(n) = A007504(n+1) - 2*A071148(n-1).

A282319 a(n) = (2097203 mod n)^2 + (2097203 mod n) + 41.

Original entry on oeis.org

41, 43, 47, 53, 53, 71, 53, 53, 71, 53, 131, 173, 61, 53, 113, 53, 281, 71, 47, 53, 347, 131, 347, 173, 53, 347, 71, 53, 151, 593, 547, 421, 461, 281, 53, 593, 83, 503, 347, 53, 197, 347, 97, 1033, 593, 347, 313, 1301, 53, 53, 1097, 1933, 2203, 71

Offset: 1

Frederic Isenmann, Feb 11 2017

This sequence gives 168 prime numbers for n=1 to 168 with 63 different primes. This formula is based on the lucky numbers of Euler.

			For n = 23, a(23) = 17^2+17+41 = 347, and 347 is prime.

Frederic Isenmann, Table of n, a(n) for n=1..168.

Cf. A005846, A202018.

Table[#^2 + # + 41 &@ Mod[2097203 , n], {n, 54}] (* Michael De Vlieger, Feb 12 2017 *)
f[n_]:=Module[{x=Mod[2097203,n]},x^2+x+41]; Array[f,60] (* Harvey P. Dale, Jul 28 2017 *)

a(n)=subst(x^2+x+41,x,2097203%n) \\ Charles R Greathouse IV, Feb 14 2017

def formul(i):
    return ((i*i+2097203)%i)*((i*i+2097203)%i)+((i*i+2097203)%i)+41
for i in range(1, 169):
    n=formul(i)
    print(n, end=", ")

cp's OEIS Frontend

User: Frederic Isenmann

A282329 Start with 2, then successively subtract the primes 3, 5, 7, ...

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Python

Formula