A085415 - OEIS

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A085415

Take prime[n] and continue adding 1, 2, ..., a(n) until one reaches a prime.

1, 4, 3, 3, 3, 3, 3, 4, 3, 12, 3, 3, 3, 4, 3, 3, 12, 3, 3, 8, 3, 4, 3, 12, 3, 3, 3, 3, 7, 8, 4, 3, 8, 4, 12, 3, 3, 4, 3, 3, 12, 4, 3, 3, 8, 7, 7, 3, 3, 4, 3, 12, 4, 3, 3, 3, 12, 3, 3, 8, 4, 11, 3, 3, 8, 8, 3, 4, 3, 4, 3, 15, 3, 3, 4, 3, 12, 8, 11, 4, 24, 4, 8, 3, 4, 3, 15, 3, 3, 7, 8, 12, 8, 11, 4, 3, 12, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Resulting primes in A085416. See also A085417, A085418.

Prime[n] plus a triangular number is prime. - Harvey P. Dale, Jun 12 2013

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

Prime[n]+m*(1+m)/2 is a prime for some m>0.

EXAMPLE

a(2)=4 because prime[2]+(1+2+3+4)=3+10=13 is a prime

MATHEMATICA

Flatten[(Sqrt[1+8#]-1)/2&/@With[{trnos=Accumulate[Range[30]]}, Table[ Select[ trnos, PrimeQ[Prime[n]+#]&, 1], {n, 100}]]] (* Harvey P. Dale, Jun 12 2013 *)

CROSSREFS

Cf. A085416, A085417, A085418.

Sequence in context: A031350 A031353 A356764 * A187470 A374419 A059124

Adjacent sequences: A085412 A085413 A085414 * A085416 A085417 A085418

KEYWORD

easy,nonn

AUTHOR

Zak Seidov, Jun 29 2003

STATUS

approved