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Where agencies said they were hiring “a few” or “many” people for a position, The Times estimated those values at five and 15, respectively, except for Forest Service positions being sought at hundreds of locations.

As a result of sequestration, the Forest Service does anticipate hiring possibly 1,000 fewer seasonal jobs this year,” spokeswoman Tiffany Holloway said in an email.

In February, Mr. Coburn, Oklahoma Republican, wrote to the Office of Management and Budget to point out that “at the same time the administration is warning sequestration could force laying off or furloughing U.S. Customs and Border Protection agents, Defense civilian employees, or food safety inspectors, the federal government is also soliciting applicants for numerous lower priority jobs.”

Mr. Coburn pointed to positions including “a counsel for the Morris K. Udall Scholarship Foundation, salary range from $130,000 to $155,000 per year,” as examples of what could be eliminated to allow the required cuts to be as painless as possible.

But as weeks of sequestration continue unabated, the positions are stacking up.

The Food and Drug Administration is hiring more than 100 people. The Department of Energy is hiring a communications specialist paying from $124,000 to $156,000.

In Omaha, Neb., alone, Veterans Affairs is looking for 12 nurse anesthetists who would make between $126,000 and $198,000 — an annual salary not out of line in that in-demand field.

But even men of the cloth who have sworn a vow of poverty appear to make good money at the federal government, with a dozen chaplain jobs paying up to $100,000 listed since sequestration.

Editor’s Note: This story was updated Tuesday.