A118134 -id:A118134 - cp's OEIS frontend

A382509 Integers s = (p1+p2)/4 such that p1 and p2 are consecutive primes and s can be written in the form p*2^k with k>=0 and p>2 prime.

3, 6, 13, 17, 28, 38, 43, 67, 80, 88, 96, 118, 127, 137, 167, 178, 188, 193, 218, 223, 272, 283, 298, 302, 328, 368, 472, 487, 508, 563, 592, 613, 617, 634, 643, 647, 662, 718, 773, 778, 802, 808, 872, 878, 932, 1033, 1142, 1168, 1172, 1187, 1193, 1198, 1256, 1277

Offset: 1

Karl-Heinz Hofmann and Hugo Pfoertner, Apr 18 2025

			For n = 2: a(n) = 6 because 4 * 6 = 24 and 24 is the sum of the two consecutive primes 11 and 13 and the factorization of 6 is 3 * 2^1.

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Cf. A001043, A118134.

Select[Plus @@@ Partition[Prime[Range[400]], 2, 1]/4, IntegerQ[#] && PrimeQ[#/2^IntegerExponent[#, 2]] &] (* Amiram Eldar, Apr 21 2025 *)

is(n) = my(v=valuation(n, 2), n2);if(!isprime(n>>v), return(0)); n2 = 2*n; n2 - precprime(n2) == nextprime(n2) - n2 \\ David A. Corneth, Apr 21 2025

from sympy import isprime, sieve as prime
A382509 = []
for x in range(2,1000):
    if (totest := (prime[x] + prime[x+1])) % 4 == 0:
        s = totest // 4
        while totest % 2 == 0: totest //= 2
        if isprime(totest): A382509.append(s)
print(A382509)

A163488 Primes p such that 5*p is a sum of 3 consecutive primes.

Original entry on oeis.org

2, 3, 47, 79, 113, 197, 227, 257, 263, 317, 347, 383, 431, 443, 491, 499, 541, 557, 617, 757, 811, 887, 929, 977, 1021, 1087, 1093, 1129, 1231, 1237, 1433, 1511, 2111, 2129, 2213, 2347, 2543, 2551, 2609, 2657, 2671, 2803, 2837, 2999, 3011, 3049, 3119, 3187

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 28 2009

nonn

Primes of the form A034961(k)/5, associated with k=1, 2, 21, 31, 42, 66,... - R. J. Mathar, Aug 02 2009

			p=2 is in the sequence because 2*5=10=2+3+5.
p=3 is in the sequence because 3*5=15=3+5+7.

Cf. A006562, A118134, A163487.

lst={};Do[If[PrimeQ[p=(Prime[n]+Prime[n+1]+Prime[n+2])/5],AppendTo[lst, p]],{n,7!}];lst
cp3Q[n_]:=Module[{mid=Floor[PrimePi[(5n)/3]],tst},tst=Total/@ Partition[ Prime[ Range[mid-10,mid+10]],3,1];MemberQ[tst,5n]]; Select[ Prime[ Range[ 500]],cp3Q]//Quiet (* Harvey P. Dale, Jan 02 2018 *)

Entries checked by R. J. Mathar, Aug 02 2009

cp's OEIS Frontend

A382509 Integers s = (p1+p2)/4 such that p1 and p2 are consecutive primes and s can be written in the form p*2^k with k>=0 and p>2 prime.

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