A147800 -id:A147800 - cp's OEIS frontend

A147801 Minimal value of A007947(m*(3^n-m)) with m coprime to 3.

2, 2, 10, 10, 22, 110, 278, 238, 1054, 1342, 11066, 6118, 18734, 107030, 557270, 163030, 1440430, 2195110, 11016290, 3641210, 23250370, 38188766

Offset: 1

M. F. Hasler, Nov 13 2008

Related to the abc conjecture. The minima are reached for m values given in A147802.

All terms of this sequence are even, so one could also consider A147801/2 = 1, 1, 5, 5, 11, 55, 139, 119, 527, 671, 5533, 3059, 9367, 53515, 278635, 81515, ...

Cf. A007947, A147298 (general case), A143702 (analog for 2^n), A147800 (analog for 5^n), A147802.

A147801(n, p=3) = {my(m=n=p^n); for(x=1, (n-1)\2, x%p || next; A007947(n-x)*A007947(x)A007947((n-x)*x)); m; }

a(17)-a(22) from Jinyuan Wang, Aug 11 2020

A147803 Least m coprime to 5 minimizing A007947(m*(5^n-m)).

Original entry on oeis.org

1, 1, 4, 49, 128, 9, 36864, 19332, 4508, 121, 2

Offset: 1

M. F. Hasler, Nov 13 2008

The minima are given in A147800.

This is related to the abc conjecture: Since m is coprime to 5, it is also coprime to 5^n and thus to 5^n-m. Thus the squarefree kernel A007947(m*(5^n-m)*5^n) = 5*A007947(m*(5^n-m)).

Cf. A007947, A147298 (general case), A147800 (value of minima), A143700 (analog for 2^n), A147802 (analog for 3^n), A147300 (analog for any number).

A147803(n,p=5) = {my(b, m=n=p^n); for(a=1, n\2, a%p || next; A007947(n-a)*A007947(a)A007947((n-a)*b=a)); b; }

A147799 Minimal value of A007947(m*(7^n-m)) with m coprime to 7.

Original entry on oeis.org

6, 6, 30, 30, 282, 2262, 17034, 36006, 71070

Offset: 1

M. F. Hasler, Nov 13 2008

The minima are reached for m values given in A147804.
This is related to the abc conjecture.
All terms of this sequence are even, so one could also consider A147799/2 = 3, 3, 15, 15, 141, 1131, 8517, 18003, 35535, ... So far these terms are also multiples of 3, but this might be a coincidence.

Cf. A007947, A147804 (m values); A143702, A147801, A147800 (analog for 2^n, 3^n, 5^n), A147298 (general case).

A147799(n,p=7)={my(m=n=p^n); for(a=1,n\2, a%p || next; m > 2*A007947(a) || next; m > A007947(n-a)*A007947(a) || next; m = A007947(n-a)*A007947(a)); m; }

A147798 Minimal value of A007947(m*(11^n-m)) with m coprime to 11.

Original entry on oeis.org

6, 30, 30, 390, 3162, 2730, 17706

Offset: 1

M. F. Hasler, Dec 06 2008

The minima are reached for m values given in A147805.

Cf. A007947, A147298, A147799, A147800, A147801, A147802, A147803, A147804, A147805.

A147798(n, p=11) = {my(m=n=p^n); for(a=1, n\2, a%p || next; m > 2*A007947(a) || next; m > A007947(n-a)*A007947(a) || next; m = A007947(n-a)*A007947(a) ); m; }

A147805 Least m coprime to 11 minimizing A007947(m*(11^n-m)).

Original entry on oeis.org

2, 1, 81, 16, 8748, 91, 1489347

Offset: 1

M. F. Hasler, Dec 06 2008

The values of the minima are given in A147798.

Cf. A007947, A147298, A147798, A147799, A147800, A147801, A147802, A147803, A147804.

/* If A147798(n) has already been computed and is stored in a147798[n]: */
A147805(n)={my(m=a147798[n]); for(a=1, n=11^n, a%11 || next; m>2*A007947(a) || next; m==A007947(a)*A007947(n-a) && return(a)) }
/* else use code from A147804 : A147805(n)=A147804(n,11) */

cp's OEIS Frontend

A147801 Minimal value of A007947(m*(3^n-m)) with m coprime to 3.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Extensions

A147803 Least m coprime to 5 minimizing A007947(m*(5^n-m)).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A147799 Minimal value of A007947(m*(7^n-m)) with m coprime to 7.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A147798 Minimal value of A007947(m*(11^n-m)) with m coprime to 11.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A147805 Least m coprime to 11 minimizing A007947(m*(11^n-m)).

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI