User:Anders Hellström/Abandoned

[Abandoned/rejected/deleted sequences]

 allocated for Anders Hellström

a(n)=gpf(A259408(n)+2) if n is odd else gpf(A259408(n)+1) 
	DATA 	

2, 3, 3, 17, 7, 139, 149, 11197, 563, 43793, 2385961, 34487
	OFFSET 	

1,1
	PROG 	

(PARI) gpf(n)=my(v=factor(n)[, 1]); v[#v];

first(m)=my(v=vector(m, x, if(m%2==1, gpf(A259408(x)+2), gpf(A259408(x)+1)))); v;
	KEYWORD 	

allocated

nonn
	AUTHOR 	

Anders Hellström, Jul 30 2015
	STATUS 	

approved

editing 

NAME 	

allocated for Anders Hellström

a(n) = gpf(1+(n-1)*n), where gpf is greatest prime factor.
	DATA 	

3, 7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 13, 307, 7, 127, 421, 463, 13, 79, 601, 31, 37, 757, 271, 67, 19, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 43, 2551, 379, 919, 409, 2971
	OFFSET 	

2,1
	LINKS 	

Anders Hellström, <a href="/A260954/b260954_1.txt">Table of n, a(n) for n = 2..10001</a>

Anders Hellström, <a href="/A260954/a260954_1.rb.txt">Ruby program</a>
	FORMULA 	

a(n) = A006530(A002061(n)). - Michel Marcus, Aug 05 2015
	MATHEMATICA 	

Table[FactorInteger[1 + n (n + 1)] [[-1, 1]], {n, 2, 60}] (* Vincenzo Librandi, Aug 05 2015 *)
	PROG 	

(MAGMA) [#f eq 0 select 1 else f[#f][1] where f is Factorization(1+n*(n+1)): n in [2..60]]; // Vincenzo Librandi, Aug 05 2015

(Sage)

def gpf(n):

    return (factor(n)[-1])[0]

def A260954vec(m): # m>2=t

      v=[]

    t=m+2

    for i in range(2, t):

        v.append(gpf(1+(i-1)*i))

    return v

(PARI) gpf(n)=my(v=factor(n)[, 1]); v[#v];

first(m)=my(v=vector(m, i, gpf(1+i*(i+1)))); v;
	CROSSREFS 	

Cf. A002583, A006530, A081256, A081257.
	KEYWORD 	

allocated

nonn,less,changed

a(1) = a(2) = 1; a(n) = a(n-2)^prime(a(n-1)) if n > 2.
(PARI) a(n)= {if(n>2, (a(n-2)^prime(a(n-1)))), 1); }

a(1) = a(2) = 1; a(n) = prime(a(n-2))^a(n-1) if n > 2.
1, 1, 2, 4, 81, 283753509180010707824461062763116716606126555757084586223347181136007
Number of digits in next term has 69 digits.
(PARI) a(n)= {if(n>2, ((prime(a(n-2))^(a(n-1)))), 1); }
Cf. A259183.

Smallest integer not a product of earlier terms nor a sum of two earlier terms.
2, 3, 7, 11, 13, 17, 23, 29, 37
cf. A047221 and A003631
=A003631

a(1)=0, for n>1 a(n) is smallest number such that for all s,t,m<n a(n) != a(s)*a(t)+a(m).
0, 1, 3, 5, 7, 11, 13, 17, 19, 23, 27, 29, 31, 37, 41, 43, 45, 47, 53, 59, 61, 63, 67, 71, 73, 75, 79, 83, 89, 97, 99, 101, 103, 105, 107, 109,
  113, 117, 125, 127, 131, 137, 139, 147, 149, 151, 153, 157, 163, 165, 167, 171, 173, 175, 179, 181
Cf. A067019, (equal to this sequence from a(3)), A000040
(PARI)
main(size)={ my(v=vector(size),r,s,t,x); v[1]=0; for(n=2, size, v[n]=v[n-1]+1; until(x==1, for(t=1, n-1, for(r=1, n-1, for(s=1, n-1, if((v[s]*v[t]+v[r])===v[n], v[n]=v[n]+1; x=0; break(3), x=1); ))))); v; } 

a(n) = gpf(1+n*(n+1)), where gpf is greatest prime factor.

(SAGE) #for 1+(n-1)*n offset 2.
from sage.all import *
import sys 

def gpf(n):
    return (factor(n)[-1])[0]
    

def a002061(k):
    return 1+k*(k-1)

def a260954(n):
    #k=2+n
    return gpf(a002061(n))

def av(m):
    t=0
    v=[]
    for k in range(t, m):
        v.append(a002061(k))
    return v 

def input():
    if len(sys.argv) != 2:
      print "Usage: %s <n>"%sys.argv[0];sys.exit(1)
    else:    
      print(av(sage_eval(sys.argv[1])));sys.exit(0) 
   
input()

NAME 	

allocated for Anders Hellström

a(n) = gpf(1+(n-1)*n), where gpf is greatest prime factor.
	DATA 	

3, 7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 13, 307, 7, 127, 421, 463, 13, 79, 601, 31, 37, 757, 271, 67, 19, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 43, 2551, 379, 919, 409, 2971, 79
	OFFSET 	

2,1
	FORMULA 	

a(n) = A006530(A002061(n+1)). - Michel Marcus, Aug 05 2015
	MATHEMATICA 	

Table[FactorInteger[1 + n (n + 1)] [[-1, 1]], {n, 2, 60}] (* Vincenzo Librandi, Aug 05 2015 *)
	PROG 	

(MAGMA) [ #f eq 0 select 1 else f[ #f][1] where f is Factorization(1+n*(n+1)): n in [2..60]]; // Vincenzo Librandi, Aug 05 2015
	CROSSREFS 	

Cf. A081256, A002583, A081257.
	KEYWORD 	

allocated

nonn,less,changed
	AUTHOR 	

Anders Hellström, Aug 05 2015
	STATUS 	

approved

proposed 

a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is factorial.
1,20,

A265015
is(s,n)=my(d=digits(n),t=1);if(#d>#s,for(i=1,#s,if(s[i]!=d[i],t=0;break)),t=0);t
remove(m,n)=my(e=1+floor(log(m)/log(10)),d=1+floor(log(n)/log(10)));n-m*(10^(d-e));
first(m)=my(v=vector(m), s=""); s="1"; v[1]=1; for(i=2, m, n=1; while(!is(digits(eval(s)), n!), n++); v[i]=remove(eval(s),n!); s=Str(n!)); v

DATA 1, 6777216
xx(n)=n^n
isxx(n)=my(i=0,j=0);if(n<2,i=1,while(xx(j)<n,j++;if(xx(j)==n,i=1;break)));i
first(m)=my(v=vector(m), s=""); s="1"; v[1]=1; for(i=2, m, n=1; while(!isxx(eval(concat(s, Str(n)))), n++); v[i]=n; s=concat(s, Str(n))); v
Cf.
keywords base,bref,more,hard

is(s,n)=my(d=digits(n),t=1);if(#d>#s,for(i=1,#s,if(s[i]!=d[i],t=0;break)),t=0);t
remove(m,n)=my(e=1+floor(log(m)/log(10)),d=1+floor(log(n)/log(10)));n-m*(10^(d-e));
first(m)=my(v=vector(m), s=""); s="1"; v[1]=1; for(i=2, m, n=1; while(!is(digits(eval(s)), fibonacci(n)), n++); v[i]=remove(eval(s),fibonacci(n)); s=Str(fibonacci(n))); v

1, 3, 46269 [index: 2,7,31]
Cf. A000045

(PARI)

 a(n)=floor(solve(x=1,n,x^x-n))
 b(n)=n-(a(n)^a(n))
 first(m)=vector(m,i,b(i))

A281301, A281302, A281303 (Hellström) too artificial - Editors, Jan 21 2017

concatenation is 10000-gonal(myriagonal) etc.

Cf. [1]