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

Author

Colin Barker, Jan 11 2018

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A054643.

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

Programs

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 *)

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)

Extensions

New name by David A. Corneth, Jan 12 2018