A298073 The first of three consecutive integers the sum of which is equal to the sum of three consecutive prime numbers.

4, 52, 156, 172, 210, 256, 262, 372, 510, 536, 562, 592, 606, 652, 732, 946, 976, 998, 1072, 1102, 1122, 1186, 1222, 1238, 1366, 1460, 1500, 1510, 1540, 1746, 1752, 1762, 1772, 1898, 1906, 1916, 2070, 2180, 2286, 2400, 2408, 2416, 2448, 2676, 2902, 2962

Offset

1,1

Comments

Also: Number m such that 3 * m + 6 is the sum of three consecutive primes. - David A. Corneth, Jan 12 2018

Links

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

Example

52 is in the sequence because 52 + 53 + 54 = 159 = 47 + 53 + 59.

Mathematica

Block[{nn = 430, s}, s = Total /@ Partition[Prime@ Range[nn], 3, 1]; Select[Partition[Range[Prime@ nn], 3, 1], MemberQ[s, Total@ #] &]][[All, 1]] (* Michael De Vlieger, Jan 11 2018 *)
(#-3)/3&/@Select[Total/@Partition[Prime[Range[500]], 3, 1], Mod[#, 3]==0&] (* Harvey P. Dale, Sep 13 2018 *)

Prog

(PARI) L=List(); forprime(p=2, 4000, q=nextprime(p+1); r=nextprime(q+1); t=p+q+r; if((t-3)%3==0, listput(L, (t-3)/3))); Vec(L)

Crossrefs

Cf. A054643.

Cf. A075540: the second of the three consecutive integers.

Sequence in context: A110908 A232507 A336428 * A233474 A297764 A101354

Adjacent sequences: A298070 A298071 A298072 * A298074 A298075 A298076

Keyword

nonn

Author

Colin Barker, Jan 11 2018

Extensions

New name by David A. Corneth, Jan 12 2018

Status

approved