

A236411


Let p(k) denote the kth prime; a(n) = smallest p(m) > p(n) such that the n2 differences between [p(n), p(n+1), ..., p(2n2)] are the same as the n2 differences between [p(m), p(m+1), ..., p(m+n2)].


2



5, 11, 13, 101, 37, 1277, 1279, 1616603, 57405419, 51448351, 76623356077, 115438255651991, 433241801791933
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


LINKS

Table of n, a(n) for n=2..14.


EXAMPLE

n=5: We take the four primes [p(5)=11, 13, 17, 19], whose successive differences are 2, 4, 2. The next time we see this sequence of differences is at [101, 103, 107, 109], so a(5) = 101.


MATHEMATICA

(* This program generates the first ten terms of the sequence. To generate more would require significantly greater computing resources *) dbp[n_]:=Differences[ Prime[ Range[ n, 2n2]]]; With[{prs=Prime[Range[ 3500000]]}, First/@ Flatten[ Table[Select[Partition[Drop[prs, n], n1, 1], Differences[#]==dbp[n]&, 1], {n, 2, 11}], 1]] (* Harvey P. Dale, Feb 05 2014 *)


PROG

(PARI) A236411 = n>{d=vector(n2, i, prime(n+i)prime(n)); forprime(p=prime(n+1), , for(k=1, #d, isprime(p+d[k])next(2)); for(k=1, #d, p+d[k]==nextprime(p+if(k>1, d[k1])+1))next(2)); return(p))} \\ The second kloop would suffice, but the first makes it 5x faster. Yields a(10), a(11) in ca. 3 sec (i7, 1.9Ghz).  M. F. Hasler, Feb 05 2014


CROSSREFS

See A073615 for a very similar sequence.
Sequence in context: A034924 A018607 A032481 * A073615 A275118 A275640
Adjacent sequences: A236408 A236409 A236410 * A236412 A236413 A236414


KEYWORD

nonn,more


AUTHOR

Don Reble, Feb 05 2014


EXTENSIONS

Edited by N. J. A. Sloane, Feb 05 2014


STATUS

approved



