A127313 Primes p such that p+q+r, where p, q, r are consecutive primes, equals s+t+1, where s and t are consecutive primes.

7, 37, 53, 59, 61, 67, 71, 83, 97, 149, 173, 181, 233, 271, 277, 283, 307, 421, 521, 541, 569, 613, 617, 673, 691, 719, 809, 859, 877, 971, 983, 1031, 1039, 1181, 1237, 1297, 1319, 1381, 1423, 1453, 1459, 1471, 1483, 1543, 1579, 1607, 1609, 1787, 1861, 1931

Offset

1,1

Comments

The smallest of three consecutive primes whose sum is equal to 1 plus the sum of two consecutive primes.

Links

Table of n, a(n) for n=1..50.

Example

37, 41, 43 are consecutive primes, 37+41+43 =121; 59 and 61 are consecutive primes, 59+61+1 = 121. Hence 37 is a term.
19, 23, 29 are consecutive primes, 19+23+29 = 71; 31 and 37 are consecutive primes, 31+37+1 = 69 < 71; 37 and 41 are the next pair of consecutive primes, 37+41+1 = 79 > 71. Hence there are no consecutive primes s and t with s+t+1 = 71 and 19 is not in the sequence.

Maple

B:={seq(1+ithprime(k)+ithprime(k+1), k=1..500)}: a:=proc(n) if member(ithprime(n)+ithprime(n+1)+ithprime(n+2), B)=true then ithprime(n) else fi end: seq(a(n), n=1..900); # Emeric Deutsch, Apr 01 2007

Prog

(Magma) [ p: p in PrimesInInterval(3, 1950) | not IsPrime(k) and PreviousPrime(k)+NextPrime(k) eq 2*k where k is (p+NextPrime(p)+NextPrime(NextPrime(p))-1) div 2 ]; /* Klaus Brockhaus, Apr 03 2007 */

Crossrefs

Sequence in context: A076285 A077720 A235463 * A217561 A003521 A155943

Adjacent sequences: A127310 A127311 A127312 * A127314 A127315 A127316

Keyword

nonn

Author

J. M. Bergot, Mar 28 2007

Extensions

Edited, corrected and extended by Emeric Deutsch and Klaus Brockhaus, Apr 01 2007

Status

approved