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A248590 Least positive integer m such that prime(m) == 1 (mod m + n). 3
3, 4, 19, 10, 5, 6, 13, 15, 7, 8, 31, 17, 9, 19, 20, 38, 22, 10, 11, 24, 78, 80, 25, 12, 28, 30, 13, 14, 599, 97, 15, 31, 32, 178, 33, 16, 102, 104, 35, 108, 17, 18, 38, 39, 361, 40, 19, 41, 73, 20, 21, 43, 45, 78, 134, 22, 391, 47, 23, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: (i) a(n) exists for any n > 0. Moreover, a(n) < n*(n-1) if n > 3.

(ii) For any n > 0, there is a positive integer m such that prime(m) == -1 (mod m + n). Moreover, we may require m < n*(n-1) if n > 1.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 19 since prime(19) = 67 == 1 (mod 19 + 3).

MATHEMATICA

Do[m=1; Label[aa]; If[Mod[Prime[m]-1, m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

CROSSREFS

Cf. A000040, A247824, A248004, A248588.

Sequence in context: A318419 A263968 A020344 * A143150 A100340 A042175

Adjacent sequences:  A248587 A248588 A248589 * A248591 A248592 A248593

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Oct 09 2014

STATUS

approved

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Last modified January 28 10:02 EST 2020. Contains 331319 sequences. (Running on oeis4.)