

A235167


Primes which are sum of the first k consecutive composite numbers and such that the sums of the first k+1, k+2 and k+3 consecutive composites are also prime.


0



1041973527756883, 1367813419317223, 2061752246097991, 2952443719006597, 3103011021307399, 3372968619197677, 10155190978946137, 34071498970634821, 43003872349213873, 45743947962658333, 58096932030228859, 60092475306807649, 115486262684753671
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OFFSET

1,1


COMMENTS

Since there are not 3 consecutive twin primes, with the exception of (3, 5, 7) because one of them would be divisible by 3; there cannot be primes sum of the first consecutive k composites, and such that the sums of the first k+1, k+2, k+3, and k+4 consecutive composites are also prime.


LINKS

Table of n, a(n) for n=1..13.


EXAMPLE

a(1) = 1041973527756883 is the least prime, sum of the first consecutive 44208182 composites from 4 to 47042265, and such that the sum of the first 44208183, 44208184 and 44208185 composites are 1041973574799149, 1041973621841417, 1041973668883687, all prime.


PROG

(PARI) i=0; b=0; for( a=2, 2*10^8, if( !isprime(a) , i=i+1; b=b+a; if(( isprime(b) &a%2==1& isprime(b+a+1)) &isprime(a+2)& isprime(b+2*a+4)&isprime( a+4)&isprime(b+3*a+9), print1(b, ", "))))


CROSSREFS

Cf. A053782, A234847, A235165.
Sequence in context: A128446 A052098 A172607 * A095431 A282672 A072719
Adjacent sequences: A235164 A235165 A235166 * A235168 A235169 A235170


KEYWORD

nonn


AUTHOR

Robin Garcia, Jan 04 2014


EXTENSIONS

a(8)a(13) from Donovan Johnson, Jan 06 2014


STATUS

approved



