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 A298102 The first of five consecutive integers the sum of which is equal to the sum of five consecutive prime numbers. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 20 07:43 EDT 2024. Contains 371799 sequences. (Running on oeis4.)