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A129699 Least nonnegative m such that P(n+3,n) + P(n+3,m) is prime where P(k,n) is n-th k-gonal number, or -1 if no such value exists. 1
2, 1, 0, 4, 2, 2, 4, 4, 2, 4, 3, 6, 73, 4, 3, 16, 9, 6, 7, 2, 17, 10, 3, 2, 10, 2, 36, 58, 9, 2, 7, 4, 6, 82, 3, 2, 25, 4, 11, 10, 2, 6, 43, 2, 14, 46, 11, 38, 37, 2, 32, 130, 14, 2, 28, 2, 5, 28, 4, 14, 37, 16, 24, 16, 2, 2, 40, 4, 2, 10, 8, 6, 46, 22, 3, 28, 5, 18, 16, 2, 26, 10, 19, 12, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define array A[k,n] for k>2, n>=0, where A[k,n] = n-th k-gonal number = k((n-2)*k - (n-4))/2. Then define array B[k,n] = least m such that the A[k,n] + m-th k-gonal number is prime. This sequence is the main diagonal of B. The array B[k,n] begins: k.|.B[k,n] 3.|..2.1.0.1.1.7.4.1.1.7.3... 4.|.-1.2.1.2.1.2.5.2.3.4.1... 5.|..2.3.0.1.1.3.4.1.4.3... 6.|.-1.1.1.4.1.4.4.2.7.4... 7.|..2.3.0.1.2.3.7.1.1.4... 8.|.-1.4.3.2.1.2.1.4.3.2... B[4,0] = -1 because 0th 4-gonal number is 0th square = 0 and 0 + c^2 cannot be prime for any integer c. B[5,6] = 4 because 6th + 5th pentagonal numbers = 51 + 22 = 73 is prime. B[8,2] = 3 because 3rd + 2nd octagonal numbers = 21 + 8 = 29 is prime.

The sequence of associated primes starts 3, 2, 5, 43, 41, 73, 157, 227, 271, 433, 541, 857, 35107, 1193, 1427,... - R. J. Mathar, Jun 12 2008

LINKS

Table of n, a(n) for n=0..85.

Eric Weisstein's World of Mathematics, Polygonal Number.

FORMULA

a(n) = min{m: m-th (n+3)-gonal number + n-th (n+3)-gonal number is prime}.

MAPLE

P := proc(k, n) n/2*((k-2)*n-k+4) ; end: A129699 := proc(n) for m from 0 to 100000 do if isprime(P(n+3, n)+P(n+3, m)) then RETURN(m) ; fi ; od: RETURN(-1) ; end: for n from 0 to 200 do printf("%d, ", A129699(n)) ; od: # R. J. Mathar, Jun 12 2008

CROSSREFS

Cf. A000040, A000217, A060354.

Sequence in context: A091453 A062173 A004558 * A002349 A096794 A106375

Adjacent sequences:  A129696 A129697 A129698 * A129700 A129701 A129702

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jun 01 2007

EXTENSIONS

Corrected and extended by R. J. Mathar, Jun 12 2008

STATUS

approved

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Last modified September 21 12:35 EDT 2019. Contains 327253 sequences. (Running on oeis4.)