A245289 -id:A245289 - cp's OEIS frontend

A258276 Balanced sphenic numbers (of order one): sphenic numbers (A007304) that are the average of the previous sphenic number and the following sphenic number.

186, 370, 406, 418, 518, 582, 602, 710, 786, 814, 826, 830, 942, 978, 994, 1010, 1034, 1070, 1162, 1310, 1374, 1394, 1570, 1630, 1686, 1758, 1886, 1978, 2014, 2114, 2158, 2270, 2274, 2278, 2294, 2438, 2510, 2534, 2570, 2630, 2666, 2690, 2774, 2778, 2782, 2806

Offset: 1

Antonio Roldán, May 25 2015

nonn

			406 is in this sequence because 406 = A007304(45) = (402+410)/2 = (A007304(44) + A007304(46))/2.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A006562, A007304, A213025, A245289.

a=30; b=42; c=66; L={}; While[ Length[L]<100, If[b-a == c-b, AppendTo[L, b]]; a=b; b=c++; While[ Last/@ FactorInteger[c] != {1,1,1}, c++]]; L (* Giovanni Resta, Jun 09 2015 *)

issphenic(n)=if(n>0,omega(n)==3&&bigomega(n)==3,0)
nextsph(n)={local(k=n+1);while(!issphenic(k),k+=1);k}
precsph(n)={local(k=n-1);while(!issphenic(k)&&k>0,k-=1);k}
{for(i=1,4*10^3,if(issphenic(i)&&2*i== nextsph(i)+ precsph(i),print1(i, ", ")))}

A245589 Primes which are the average of the two adjacent primes and also of the two adjacent squarefree numbers.

Original entry on oeis.org

53, 593, 1747, 2287, 4013, 4409, 5563, 6317, 8117, 10657, 10853, 11933, 12547, 12583, 12653, 15161, 16937, 17047, 17851, 18341, 19603, 19949, 20107, 22051, 26693, 31051, 32993, 35851, 35911, 39113, 42209, 42533, 44041, 46889, 47527, 48259, 50417, 51461

Offset: 1

Juri-Stepan Gerasimov, Jul 26 2014

nonn

Intersection of A006562 and A240475. Intersection of A006562 and A245289.

			53 is in this sequence because 53 = prime(16) = (prime(15) + prime(17))/2 = (47 + 59)/2 and 53 = squarefree(33) = (squarefree(32) + squarefree(34))/2 = (51 + 55)/2.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A006562, A240475, A245289.

Primes:= select(isprime,[$1..10^5]):
Sqfree:= select(numtheory:-issqrfree,[$1..10^5]):
A:= NULL:
for i from 2 to nops(Primes)-1 do
   if Primes[i] = (Primes[i+1]+Primes[i-1])/2 then
      member(Primes[i],Sqfree,'j');
      if Primes[i] = (Sqfree[j-1]+Sqfree[j+1])/2 then
         A:= A,Primes[i]
      fi
   fi
od:
A; # Robert Israel, Aug 21 2014

maxp=60000;
p=[]; my(v=primes(maxp)); for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], p=concat(p, v[k]))); p;
v = select(n->issquarefree(n), vector(maxp, n, n));
s=[]; for(k=2, #v-1, if(2*v[k] == v[k-1]+v[k+1], s=concat(s, v[k]))); s;
setintersect(p, s) \\ Colin Barker, Aug 07 2014

Missing term (16937) inserted by Colin Barker, Aug 07 2014

cp's OEIS Frontend

A258276 Balanced sphenic numbers (of order one): sphenic numbers (A007304) that are the average of the previous sphenic number and the following sphenic number.

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