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User:Anders Hellström/Abandoned
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[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]