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.

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

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, vc-1, 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