A298102 The first of five consecutive integers the sum of which is equal to the sum of five consecutive prime numbers.

77, 279, 293, 327, 347, 353, 401, 437, 509, 641, 675, 683, 785, 803, 839, 885, 947, 961, 1169, 1177, 1193, 1239, 1325, 1337, 1395, 1433, 1461, 1501, 1545, 1639, 1683, 1715, 1731, 1777, 1809, 1915, 1955, 1989, 2031, 2059, 2139, 2145, 2345, 2387, 2393, 2431

Offset

1,1

Comments

Also: Number m such that 5 * m + 10 is the sum of 5 consecutive primes. - David A. Corneth, Jan 12 2018

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Example

77 is in the sequence because 77+78+79+80+81 = 395 = 71+73+79+83+89.

Mathematica

p = {2, 3, 5, 7, 11}; lst = {}; While[p[[1]] < 3001, t = Plus @@ p; If[Mod[t, 10] == 5, AppendTo[lst, (t - 10)/5]]; p = Join[Rest@p, {NextPrime[p[[-1]]]}]]; lst (*  Robert G. Wilson v, Jan 14 2018 *)
Select[(#-10)/5&/@(Total/@Partition[Prime[Range[400]], 5, 1]), IntegerQ] (* Harvey P. Dale, Jun 22 2019 *)

Prog

(PARI) L=List(); forprime(p=2, 2500, q=nextprime(p+1); r=nextprime(q+1); s=nextprime(r+1); t=nextprime(s+1); u=p+q+r+s+t; if((u-10)%5==0, listput(L, (u-10)\5))); Vec(L)
(PARI) upto(n) = my(res = List(), pr = primes(5), s = vecsum(pr)); while(pr[5] < n, if(s == 5 * pr[3], listput(res, pr[1])); lp = nextprime(pr[5] + 1); s += (lp - pr[1]); for(i = 1, 4, pr[i] = pr[i+1]); pr[5] = lp); res \\ David A. Corneth, Jan 12 2018

Crossrefs

Cf. A054643, A298073, A298103.

Sequence in context: A255095 A029558 A156652 * A158767 A158771 A331976

Adjacent sequences: A298099 A298100 A298101 * A298103 A298104 A298105

Keyword

nonn

Author

Colin Barker, Jan 12 2018

Extensions

New name by David A. Corneth, Jan 12 2018

Status

approved