A077287 If the least prime factor of ((prime(k)*prime(k+1))^2 + 1)/2 for k >= 2 is not yet in the sequence, then add it to the sequence.

113, 613, 5, 24421, 101, 2042221, 13, 41, 60731221, 102975601, 6653, 253102501, 327449641, 17, 14957, 722798221, 37, 35597, 797, 233, 2284271641, 7937, 337, 73, 29, 53, 46414646521, 57358506301, 2521, 89, 89249322541, 61, 281, 56597

Offset

1,1

References

C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory, Dover, New York, 1988.

Links

Table of n, a(n) for n=1..34.

Mathematica

PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; a = {}; Do[l = PrimeFactors[((Prime[n]*Prime[n + 1])^2 + 1)/2]; If[ Position[a, l[[1]]] == {}, AppendTo[a, l[[1]]]], {n, 2, 127}]; a

Prog

(PARI) f(k) = vecmin(factor(((prime(k)*prime(k+1))^2 + 1)/2)[, 1]);
lista(nn) = my(list=List()); for (n=2, nn, my(fn = f(n)); if (!vecsearch(vecsort(Vec(list)), fn), listput(list, fn)); ); Vec(list); \\ Michel Marcus, May 14 2025

Crossrefs

Sequence in context: A109563 A142024 A300964 * A087294 A152928 A185337

Adjacent sequences: A077284 A077285 A077286 * A077288 A077289 A077290

Keyword

nonn

Author

Bill McEachen, Aug 22 2003

Extensions

Edited by Robert G. Wilson v, Sep 27 2003

Entry revised by Sean A. Irvine, May 14 2025

Status

approved