

A078425


Primes in "Ulam's Prime sequence". A prime is in the sequence iff p+1 can be expressed in exactly 1 way as the sum of 2 previous distinct primes.


1



3, 5, 7, 11, 13, 19, 29, 41, 43, 59, 83, 89, 107, 109, 127, 139, 157, 163, 173, 199, 211, 223, 257, 271, 277, 293, 307, 331, 347, 367, 397, 421, 443, 457, 491, 541, 557, 587, 601, 631, 691, 761, 769, 821, 911, 941, 971, 991, 1009, 1033, 1103, 1129, 1153, 1201
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(1) = 3, a(2) = 5; for n >= 3, a(n) is smallest prime which is uniquely a(j) + a(k)  1, with 1<= j < k < n.
Is the (3,5) sequence finite or infinite? Note that (3,7) as a starting sequence has only 2 terms and (7,11) yields 7, 11, 17, 23, 29 only. Equally using 1 as a rule creates more variants.
The sequence continues at least up to a(2227) = 400031.
After about 500 terms, the graph of this sequences appears almost linear.  T. D. Noe, Jan 20 2008


LINKS

T. D. Noe, Table of n, a(n) for n=1..10000
Index entries for Ulam numbers


EXAMPLE

a(3)=7 as 8=3+5. a(4)=11 as 12=5+7 (and nothing else).


PROG

(PARI) v=vector(1220); vc=2; v[1]=3; v[2]=5; forprime (p=7, 1220, p1=p+1; pc=0; fl=0; for (i=1, vc1, for (j=i+1, vc, if (v[i]+v[j]==p1, pc++); if (pc>1, fl=1); if (fl, break)); if (fl, break)); if (pc==0, fl=1); if (!fl, vc++; v[vc]=p)); print(vecextract(v, concat("1..", vc)))


CROSSREFS

Cf. A002858 (Ulam numbers), A002859, A003666, A003667, A001857, A048951, A007300.
Sequence in context: A059353 A212375 A040993 * A020587 A249077 A126960
Adjacent sequences: A078422 A078423 A078424 * A078426 A078427 A078428


KEYWORD

nonn


AUTHOR

Jon Perry, Dec 29 2002


EXTENSIONS

Edited and extended by Klaus Brockhaus, Apr 14 2005


STATUS

approved



