A298102 - OEIS

%I #23 Jun 22 2019 16:50:53

%S 77,279,293,327,347,353,401,437,509,641,675,683,785,803,839,885,947,

%T 961,1169,1177,1193,1239,1325,1337,1395,1433,1461,1501,1545,1639,1683,

%U 1715,1731,1777,1809,1915,1955,1989,2031,2059,2139,2145,2345,2387,2393,2431

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

%C Also: Number m such that 5 * m + 10 is the sum of 5 consecutive primes. - _David A. Corneth_, Jan 12 2018

%H Colin Barker, <a href="/A298102/b298102.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 *)

%t Select[(#-10)/5&/@(Total/@Partition[Prime[Range[400]],5,1]),IntegerQ] (* _Harvey P. Dale_, Jun 22 2019 *)

%o (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)

%o (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

%Y Cf. A054643, A298073, A298103.

%K nonn

%O 1,1

%A _Colin Barker_, Jan 12 2018

%E New name by _David A. Corneth_, Jan 12 2018