Kishin Ikemoto - cp's OEIS frontend

User: Kishin Ikemoto

Kishin Ikemoto has authored 2 sequences.

A376740 Numbers that have at least one two-digit prime factor.

11, 13, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 102, 104, 106, 110, 111, 114, 115, 116, 117

Offset: 1

Kishin Ikemoto, Oct 03 2024

Subsequence of A068191, first differing at A068191(55) = 101 which is not a term here.
Numbers k such that gcd(k,10978895066407230594062391177770267) > 1. - Chai Wah Wu, Nov 18 2024 [The big number is A109819(10) - Alois P. Heinz, Nov 18 2024]
The asymptotic density of this sequence is A051953(A109819(10))/A109819(10) = 1329644281346285477858013527/2807455661493975149742813527 = 0.473611... . - Amiram Eldar, Nov 19 2024

			201 = 3*67 is in this sequence because it has one two-digit prime factor.
202 = 2*101 is not, because neither of them is two-digit.

Kishin Ikemoto, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, order 10978895066407230594062391177770267.

Cf. A051953, A068191, A084891, A109819.

q:= convert(select(isprime, [seq(i,i=11 .. 99, 2)]),`*`):
filter:= n -> igcd(n,q) > 1:
select(filter, [$1..200]); # Robert Israel, Nov 18 2024

A376740Q[k_] := GCD[k, 10978895066407230594062391177770267] > 1;
Select[Range[200], A376740Q] (* Paolo Xausa, Jun 24 2025 *)

is(k) = {forprime(p = 11, 97, if(!(k % p), return(1))); 0;} \\ Amiram Eldar, Nov 19 2024

def ok(n): return any(n%p == 0 for p in [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97])
print([k for k in range(1, 118) if ok(k)]) # Michael S. Branicky, Oct 15 2024

a(n + A051953(A109819(10))) = a(n) + A109819(10). - Amiram Eldar, Nov 19 2024

A374507 Prime numbers that precede and follow consecutive balanced primes.

Original entry on oeis.org

7829, 32491, 40087, 40099, 50423, 104009, 128461, 166967, 167747, 169307, 186259, 203011, 206209, 245759, 253987, 260387, 267581, 295271, 297403, 311021, 331159, 336163, 353081, 370009, 381389, 396079, 396449, 442843, 455431, 481513, 577867, 596599, 605861

Offset: 1

Kishin Ikemoto, Jul 09 2024

nonn

			7817, 7823, 7829, 7841, and 7853 are consecutive primes. Since 7823 and 7841 are consecutive balanced primes (7817 + 7829 = 2*7823, 7829 + 7853 = 2*7841), 7829 is in this sequence.

Kishin Ikemoto, Table of n, a(n) for n = 1..10000

Cf. A006562 (balanced primes).

#include 
#define K 5
#include 
int main(void) {
    int x[K], primej, z, md, n, maxd, count;
    x[0] = 2; x[1] = 3; x[2] = 5; x[3] = 7; x[4] = 11;
    primej = 1;
    n = 13;
    maxd = 3;
    count = 0;
    while (count < 50) {
        for (md = 2; md <= maxd; md++) {
            if (n % md == 0) {
                primej = 0;
            }
        }
        if (primej == 1) {
            x[0] = x[1]; x[1] = x[2]; x[2] = x[3]; x[3] = x[4]; x[4] = n;
            if (x[0] + x[2] == 2 * x[1] && x[2] + x[4] == 2 * x[3]) {
                z = x[2];
                count++;
                printf("%d %d\n", count, z);
            }
        }
        n += 2;
        maxd = sqrt((double)n);
        primej = 1;
    }
    return 0;
}

p,q,r,s,t:= 2,3,5,7,11:
count:= 0: R:= NULL:
while count < 40 do
 p,q,r,s:= q,r,s,t;
 t:= nextprime(t);
 if p+r = 2*q and r+t = 2*s then
   count:= count+1;
   R:= R,r;
 fi;
od:
R; # Robert Israel, Jul 11 2024

Select[Partition[Prime[Range[50000]],5,1],#[[2]]==(#[[1]]+#[[3]])/2&&#[[4]]==(#[[3]]+#[[5]])/2&][[;;,3]] (* Harvey P. Dale, Sep 17 2024 *)

cp's OEIS Frontend

User: Kishin Ikemoto

A376740 Numbers that have at least one two-digit prime factor.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula