Kevin D. Woerner - cp's OEIS frontend

User: Kevin D. Woerner

Kevin D. Woerner has authored 2 sequences.

A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k).

7, 12, 14, 18, 22, 38, 58, 158, 178, 382, 502, 542, 718, 878, 1202, 1318, 1382, 1438, 1622, 1822, 2018, 2558, 2578, 2858, 2902, 3062, 3118, 3778, 4282, 4358, 4442, 4678, 4702, 5078, 5098, 5582, 5638, 5702, 5938, 6338, 6638, 6662, 6718, 6998, 7418, 8222, 8782, 8818, 9182, 9662, 9902

Offset: 1

Kevin D. Woerner, Aug 03 2018

nonn

Besides the 1st, 2nd, and 4th terms, a(n) is 2 times a prime, one of a(n)-1 or a(n)+1 is a prime, and the other number is 3 times a prime.

The 10 in the definition is the smallest value for which this is a possibly infinite list.

			For a(3)=14, sigma_0(13)=2, sigma_0(14)=4, and sigma_0(15)=4, hence sigma_0(a(3)-1) + sigma_0(a(3)) + sigma_0(a(3)+1) = 10.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005.

Res:= 7,12,14,18: count:= 4:
p:= 9:
while count < 100 do
  p:= nextprime(p);
  n:= 2*p;
  if n mod 3 = 1 then v:= isprime(n+1) and isprime((n-1)/3)
  else v:= isprime(n-1) and isprime((n+1)/3)
  fi;
  if v then count:= count+1; Res:= Res, n fi
od:
Res; # Robert Israel, Aug 27 2018

Select[Partition[Range[10^4], 3, 1], Total@ DivisorSigma[0, #] == 10 &][[All, 2]] (* Michael De Vlieger, Aug 05 2018 *)

isok(n) = numdiv(n-1) + numdiv(n) + numdiv(n+1) == 10; \\ Michel Marcus, Aug 04 2018

A317650 The n-th term is the smallest integer > 1 that is congruent to +1 or -1 modulo k for all 2 <= k <= n.

Original entry on oeis.org

3, 5, 5, 11, 11, 29, 41, 71, 71, 881, 1079, 10009, 10009, 32759, 82081, 636481, 636481, 2162161, 2162161, 2162161, 2162161, 39412801, 39412801, 39412801, 39412801, 1074427199, 1074427199, 15362146799, 15362146799, 109271408401, 482955026399, 482955026399

Offset: 2

Kevin D. Woerner, Aug 02 2018

nonn

Rest@ Nest[Function[a, Append[a, Block[{k = a[[-1]]}, While[! AllTrue[Table[Or[# == 1, # == m - 1] &@ Mod[k, m], {m, Length@ a + 1}], # &], k++]; k]]], {2}, 16] (* Michael De Vlieger, Aug 02 2018 *)

ok(n,m)={for(i=2, n, my(r=m%i); if(r<>1&&r<>i-1, return(0))); 1}
a(n)={my(m=oo, p=primes(primepi(n))); p=vector(#p, i, p[i]^logint(n, p[i]));
for(k=0, 2^#p-1, my(t=2+lift(-2+chinese(vector(#p, i, Mod(if(bittest(k, i-1), -1, 1), p[i]))))); if(tAndrew Howroyd, Aug 02 2018

a(21)-a(32) from Andrew Howroyd, Aug 02 2018

cp's OEIS Frontend

User: Kevin D. Woerner

A317670 Numbers k such that sigma_0(k-1) + sigma_0(k) + sigma_0(k+1) = 10, where sigma_0(k) = A000005(k).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI