A076537 - OEIS

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A076537

Map positive rational numbers to positive integers by diagonal method using c(p,q) = (p + q - 2) * (p + q - 1) / 2 + p where p and q are positive integers. a(n) is an increasing sequence including all c(p,q) where gcd(p,q) > 1.

5, 12, 13, 14, 23, 25, 27, 31, 34, 38, 40, 41, 42, 44, 57, 58, 59, 61, 63, 64, 65, 80, 82, 84, 85, 86, 88, 90, 94, 96, 97, 100, 101, 103, 107, 109, 111, 113, 115, 117, 119, 138, 139, 140, 142, 144, 145, 146, 148, 150, 151, 152, 173, 175, 176, 177, 179, 181, 183

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

a(1) = c(2,2) = (2 + 2 - 2) * (2 + 2 - 1) / 2 + 2 = 5 because gcd(2,2) = 2 > 1.

a(2) = c(2,4) = (2 + 4 - 2) * (2 + 4 - 1) / 2 + 2 = 12 because gcd(2,4) = 2 > 1.

PROG

(PARI) a(n)=if(n<1, 0, n=a(n-1); until(1<gcd(n-binomial(floor(1/2+sqrt(2 *n)), 2), binomial(floor(3/2+sqrt(2*n)), 2)-n+1), n++); n)

CROSSREFS

Sequence in context: A268035 A223255 A367573 * A263580 A110134 A014156

Adjacent sequences: A076534 A076535 A076536 * A076538 A076539 A076540

KEYWORD

nonn

AUTHOR

Robert A. Stump (bee_ess107(AT)msn.com), Oct 18 2002

STATUS

approved